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THE
LOGIC OF SCIENCE
A TRANSLATION
POSTERIOR ANALYTICS OF ARISTOTLE,'
WITH NOTES AND AN INTRODUCTION.
BY
EDWARD POSTE, M.A.
FELLOTV OF OBIEL COLLEGE.
OXFORD:
FRANCIS MACPHBRSON.
MDCCCL.
1 UNSVERSITV I
\LIBRARY.^ -'
PREFACE.
There is a pretty general agreement among those who have
devoted any attention to Logic, that the Logical works of
Aristotle would repay the labour of a perusal. In spite, how-
ever, of this opinion, it does not appear that the pages of the
Organon are often turned over by very diligent hands. Nor is
this very difficult to be accounted for, if we consider their
obscurity — a quality, indeed, which they share with most of
Aristotle's productions. It was to facilitate the study of the
original that this translation of a portion of it was undertaken :
and the Posterior Analytics was the portion selected, both
because it is intrinsically the most valuable, as affording the
greatest insight into Aristotle's views, and bringing him on to
the same ground with modem writers on the Philosophy of
Science ; and because the remaining parts are already tolerably
weU known through the works of the Scholastic logicians,
while this, though far more interesting to a student of the
Baconian Logic, has been comparatively neglected. In the
Introduction a sketch has been given of the whole of the
Organon.
ERRATA.
Page 18, Note ' for ^ /liaovg twoq, read ^ fispovQ nvog.
47, Note " for System of Logic, BOOK II. read System of Logic,
BOOK III.
. 113, Note • for The conclusion deducted, read The conclusion de-
duced.
114, for CHAPTER XII. read CHAPTER XI.
117, for CHAPTER XIII. read CHAPTER XII.
121, for CHAPTER XIV. read CHAPTER XIII.
126, for CHAPTER XVI. read CHAPTER XV.
ADDENDUM.
Page 4, to Note ', add traaa yap in-iarriiiri xai ivvajtii rov PeXriarov
SoKfT ttvai. Topics, \i. 5.
CONTENTS
INTRODUCTION.
Page
§ 1. 2. Idea of Logic gathered from modern writers.. . 1
3. Sketch of the Organon. General Logic 8
4. Logic of Deduction 10
5. Logic of Opinion 16
6. Logic of Induction 31
POSTERIOR ANALYTICS.
BOOK I.
Chap. I. Infekence 39
§ 1 . All Inference implies Antecedent knowledge.
2. Reducible to three classes.
3. "When a conclusion is particular, the minor pre-
miss is rather Simultaneous, than Antecedent.
4. The Antecedent knowledge of a conclusion is only
Implicit.
Chap. II. Scientific Peincipies 41
§1. Definition of Science.
2. 3. Scientific principles are indemonstrable,
4. Causal, and absolutely Antecedent,
5. and Appropriate.
6. Are divisible into Axioms and Theses : the latter
are Definitions or Hypotheses.
7. Possess higher evidence than the Conclusions.
Chap. III. Some tetjths ake Indemonsteabie. . . 43
§ 1 . Two opinions on Demonstration — that it is Impos-
sible ; and that it is Circular.
2. Arguments against the latter opinion.
Chap. IV. Univebsal, Essential, Commensueate. . . 44
§ 1. The premisses of Science are necessary.
2. Definition of Universal.
vi CONTENTS.
Paciii
§ 3. Two kinds of Essential : the latter kind is neces-
sary by the Axiom.
4. Definition of Commensurate.
Chap. V. Commensukate Peopositions 46
§ 1. A Commensurate proposition is Essential, and dis-
tributes the predicate.
2. A Commensurate subject is the lowest ineliminable
genus.
Chap. VI. Scientipic Peinciples ake Essential. . . 48
§ 1. Because they are Necessary.
2. Arguments to show that Scientific principles are
Necessarj'.
3. A conclusion from Contingent premisses is only
Hypothetically Necessary.
4. Scientific principles are Essential because they are
Causal.
Chap. VII. Scientific Peinciples aee Appeopeiate
AND Intkansfeeable 50
§ 1. Only the Axioms are common to heterogeneous
sciences ; for the other principles are Essential.
2. Sciences only examine their Appropriate problems.
Chap. VIII. Scientieic Peinciples aee Eteenal. . . 51
Chap. IX. Theee is no Uniyeesal Science 52
§ 1. Scientific principles are Peculiar to the subject-
matter, because the conclusions are Essential.
2. They are common to Generic and Specific sciences
only.
3. No Universal science can demonstrate the Appro^
priate or Specific principles of the particular
sciences.
Chap. X. Hypotheses 54
§ 1. An Hypothesis agserts the Existence of an elemen-
tary substance or power.
2. Axioms need not be expressed in their most
universal form.
CONTENT^.
Page
§ 3. The Predicate is only assumed in Definition : the
Subject both in Definition and Hypothesis.
4. Three elements, though not always expressed, are
essential to all sciences.
5. Hypothesis difiers from Axiom.
6. Postulate and Relative Hypothesis.
7. Hypothesis difiers from Definition, and from the
suppositions of the geometer with respect to
bis Diagrams.
Chap. XI. Axioms 56
§ 1. Universals are indispensable to science ; but not
the Platonic Ideas.
2. The Axioms are not expressed, but implied. The
principle of Direct proof, that both of two Con-
tradictories cannot be true.
The terms of syllogism are not necessarily Com-
mensurate.
3. The principle of Indirect proof, that one of two
Contradictories must be true.
4. The Axioms are common to all the sciences, to
Dialectics, and to Metaphysics.
Chap. XII. PECULiAEiTiEs of Science 57
§ 1. The Geometrician is not bound to argue with one
who disputes his principles, nor to discuss
extrageometrical questions.
2. Two senses of ungeometrical.
3. Geometry not liable to Dialectical fallacies.
Instance of fallacy of Consequens.
4. Why Analytical reasoning is possible in Mathe-
matics.
5. Exainple.^ofJhe Synthetical process.
Chap. XIII. Fact and Reasoned Fact, or Induction
AND Deduction 60
§ 1. Two kinds of Fact-conclusion.
2. Examples of Fact-conclusion which involve a Rea-
soned conclusion.
3. Examples of Fact-conclusion which involve no
Reasoned'conclusion.
viii CONTENTS.
PAGE
§ 4. The Fact and Reason may belong to different
Sciences.
Chap. XIV. The fikst Figuee is the most Scientific. 63
Chap. XV. Indemonstrable Negatives 64
§ 1. A negative is indemonstrable if both its terms are
summa genera.
Chap. XVI. Eekok in Peinciple 65
§ 1 . May be founded on supposed proof.
2. If the conclusion is a universal afBrmative, either
both premisses, or the minor singly, may be
false.
3. If the conclusion is a universal negative, in the
first figure, both premisses, or either singly,
may be false.
4. In the second figure, both premisses cannot be
contraries of the truth.
5. But both may be contradictories of the truth.
6. And either singly may be contrary.
Chap. XVII. Eekok in Conclusion 68
§ 1. If the true conclusion is affirmative, and the syl-
logism in the first figure ; when the middle is
appropriate, only the major can be false.
2. When the middle is inappropriate the major may
be false and the minor true :
3. Or both false:
4. Or the major true and minor false.
5. In the second figure both cannot be contraries of
the truth, but either may.
6. If the true conclusion is negative, when the
middle is appropriate, only the major can be
false.
7. When the middle is inappropriate, the major alone
may be false.
8. The minor alone may be false.
9. Or both may be false.
CONTENTS. ix
Paoe
Chap. XVIII. Beginning of Knowledge 70
§ 1. All science is founded on Induction.
Chap. XIX. Abe ant Tbuths by theib own natuee
Indemonsteabie ? 70
§ 1. Difference of Proper and Improper predication.
2. Is the process of Generalization finite ?
3. Is the process of Specification finite ?
4. Are the intermediates between two given extremes ~
finite ?
5. The same questions in negative proof.
6. In a circle of terms none are Antecedent or Ulti-
mate.
Chap. XX. When the Exibemes aee given, . . . . 72
§ 1. the Intermediates are Finite,
2. and continuous.
Chap. XXI. Negative Peopositions 72
§ 1. If the trains of Generalization and Specification
implied in the proof of an afiirmative proposi-
tion are finite, those implied in the proof of a
negative proposition are finite.
2. Shown in the first figure.
3. In the second figure.
4. In the third figure.
5. The trains would be limited, even though each
conclusion were drawn in every possible mood
and figure with different terms.
Chap. XXII. The Teains aee Finite 75
§ 1. Dialectical Proof: if the train of Generalization
were infinite, Essences would be indefinable.
2. Distinction of Proper and Improper Predication.
3. Predication Proper is Substantive or Attributive.
4. Predication Proper is not Circular.
5. Rectilinear predication is finite : for both the
generalization of Substances and that of Attri-
butes is finite ; and therefore their sum is finite.
6. Second Dialectical proof: if no truths were Im-
mediate, all conclusions would be Hypothe-
tical.
X CONTENTS.
Paob
§ 7. Scientific proof: two kinds of essential predica-
tion, Substantive and Attributive.
8. The Attributive nexus is finite.
9. The Substantive nexus is finite.
10. Demonstration is possible, and rests on indemon-
strable truths.
Chap. XXIII. Ultimate Laws 78
§ 1. Two subjects may have an immediate connection
with the same predicate.
2. Immediate laws are the Elements of Deduction,
and cannot be discovered by a Deductive pro-
cess.
3. Immediate laws are the ultimate Atoms of science.
4. The proof of a negative involves no term higher
than the major.
Example in the first figure in Celarent.
5. Example in the second figure in Camestres.
6. Example in the third figure in Bokardo.
Chap. XXIV. Compaeison of Paeticuxab and Com-
mensurate Pkoof 81
§ 1. 2. 3. Particular proof may seem more perfect, as
being Essential, and not Delusory.
4. 5. But Particular proof is not Essential, and Com-
mensurate is not Delusory.
6. 7. It shows the Cause and ultimate Reason.
8. 9. 10. Is Antecedent : contains the particular vir-
tually: and is an object of Reason not of Sense.
Chap. XXV. Comparison op Appiemative and Nega-
tive Peoop . . 84
§ 1. Afiirmative proof employs fewer premisses.
2. Needs no Negative premisses.
3. 4. Is Prior and more Elementary.
Chap. XXVI. Compaeison op Dieect and Indirect
Proof 86
§ 1 . Nature of Indirect proof.
2. It does not rest on absolutely antecedent pre-
CONTENTS. xi
Page
Chap. XXVII. Compabative Peepection of Sciences. 87
§ 1. A perfect science gives the Reason, not merely
the Fact.
2. Is Abstract :
3. and Elementary.
Chap. XXVIII. Unity of Science 87
§ 1. Identity Generic or Specific.
2. Tests of Unity.
Chap. XXIX. Diteksitt of Peoof 88
§ 1. The same conclusion is susceptible of several
proofs.
Chap. XXX. Chance 88
§ 1. A matter of chance cannot be proved.
Chap. XXXI. Sensation 89
§ 1. Sensation is not Science, because Incommensurate.
2. Yet is sometimes preferable to Science.
3. and might sometimes supersede Scientific inquiry.
Chap. XXXII. Muitipmcity of Scientific Prin-
ciples 90
§ 1. Dialectical proof: some are true, others false.
2. Scientific proof: Heterogeneous terms cannot enter
into the line of predication ; and the common
principles, or Axioms, are insufiicient to prove
the characteristic conclusions of a science.
3. The number of Premisses nearly equals the num-
ber of Conclusions.
4. As conclusions are infinite, and homogeneous
terms are finite, the heterogeneous terms must
be infinite.
5. Some principles are contingent, others necessary.
6. 7. Every science has at least one Peculiar law.
8. Principles cannot be even Generically the same.
Chap. XXXIII. Science and Opinion 93
§ 1 . The conclusions of Science are necessary.
2. The ultimate grounds of Science are Definitions.
3. How far the objects of Science and Opinion may be
the same.
xii CONTENTS.
§ 4. Science and Opinion are incompatible in the same
mind.
Chap. XXXIV. Sagacity 95
§ 1. is a rapid perception of the cause of a given phae-
nomenon.
BOOK II.
Chap. I. Problems of Science 96
§ 1. Four kinds of Problem: the problem of Fact, of
Reason, of Existence, of Essence.
2. Problem of Fact.
3. Problem of Reason.
4. Problem of Existence.
5. Problem of Essence.
Chap. II. The Object of Inquiry is always the
Intermediate. 97
§ 1. In the Problems of Fact and Existence we ask, Is
there an Intermediate ?
2. In the Problems of Reason and Essence we ask.
What is the Intermediate ?
3. The Problems of Fact and Existence are similar.
4. The Problems of Reason and Essence are similar.
5. The object of inquiry is always the Intermediate.
Chap III. Definition and Demonstration have
NOT the same province 98
§ 1. 2. 3. 4. 5. 6. Definition and Demonstration cannot
have the same province, for unity of truth im-
plies unity of knowledge, &c.
7. And because Definitions are the basis of Demon-
stration ;
8. and are assumed.
9. In Definition there is no subject and predicate.
10. Definition gives an Essence, Demonstration a
Fact.
Chap. IV. Categorical Proof of a Definition .... 101
% 1. Involves z, petitio principii.
CONTENTS. xiii
Paob
Chap. V. Establishment of Definition by Division 102
§ 1 . The proof of a Definition by Division involves a
petiiio prindpii at every stage :
2. and at the end.
3. Its completeness may be ensured.
4. 5. Some conclusion results from a Division, but
no Definition.
Chap. VI. Hypothetical Pboof of Definition, and
PBOOF BY Definition of the Opposite 103
§ 1 . Hypothetical proof of a Definition involves a pe-
tiiio prindpii.
2. As we do not quote the Axiom to prove, so we
ought not to define Definition in order to de-
fine a particular object.
3. Proof by Definition of the Opposite involves a
petiiio prindpii.
4. Neither proof by Hypothesis nor proof by Division
accounts for the Unity of the object defined.
Chap. VII. Essence cannot be Pkoved .. .. .. 104
§ 1. Essence is not the object of Deduction, Induction,
nor Sensation.
2. Essence involves Existence, which cannot be the
object of Definition, because Definition can
only give a single truth.
■ 3. Besides, Existence is the object of Demonstration.
4. There is no cogency in Definition, either as to the
Existence of the object, or as to the Significa-
tion of the word.
5. Signification is not the object of Definition.
6. Definition is not demonstrative, nor can Essence
be discovered by Definition.
Chap. VIII. Two kinds of Definition . . ^ . . . 107
§ 1 . Categorical proof of a Definition involves a peti-
iio prindpii, and is Dialectical.
2. Knowledge of the Essence never precedes know-
ledge of the Existence.
xiv CONTENTS.
Page
§ 3. Knowledge of Existence sometimes implies a par-
tial knowledge of the Essence, sometimes is
Accidental.
4. Knowledge of Existence may imply a knowledge
of the causal part^of the Essence.
5. Or it may imply no knowledge of the Essence.
6. The Essence is the reason of the Existence.
7. The Definition of the Elementary is not ana-
lyzable into cause and effect.
Chap. IX. Foub kinds op Depinition 110
§ 1 . Verbal Definition.
2. Unity of Statement.
3. Real Definition of the mediate, stating the cause.
4. Omitting the cause.
5. Definition of the Immediate.
Chap. X. Causation .• Ill
§ 1 . Four kinds of cause.
2. The Material cause.
3. The Formal cause.
4. The Eificient cause.
5. The Final cause.
6. The Final cause inverts the chronological order.
7. The Final cause is reconcilable with the Mate-
rial.
8. Two kinds of Necessity.
9. Chance.
Chap. XI. Succession of Cause and Eppect 114
§ 1 . Cause and Effect may be synchronous,
2. Or successive ; in which case the cause may be
inferred from the effect,
3. But not the effect from the cause.
4. Present and Past events are discontinuous.
5. The media to infer an Antecedent from a Conse-
quent are infinite,
6. Whether both events are past, or both future.
7. Example.
CONTENTS. XV
Page
§ 8. Natural occurrences proceed in Cycles similar to
Circular Reasoning.
9. General premisses give General conclusions.
Chap. XII.* Establishment or Definition 117
§ 1. Essence consists of predicates confined to the
genus, and distinguishing the species.
2. It may he proved Hyppthetically.
3. The foundation of Deductive Science Definitions
of the Elementary.
4. Division shows the order of the essential ele-
ments :
5. and ensures completeness.
6. Definition does not imply universal knowledge.
7. The essential character of the predicates included
must be ensured by Dialectical topics.
8. Mode of determining their order ;
9. And of ensuring completeness.
10. Inductive mode of discovering the Definition.
11. Subgenera must be defined before the genus.
Chap. XIII.* Antecedent Laws 121
§ 1. Our data should be arranged according to their
degree of generality.
2. We should endeavour to discover new genera :
3. and to trace new analogies.
4. Problems are the same generically or specifically :
5. or if related as antecedent and consequent.
Chap. XIV. Relation of Cattse and Effect . .
§ 1. Cause and Efiect reciprocate as media of proof :
2. at least if the cause is commensurate.
3. The same effect has only one essential cause.
4. Acause,likeaneffect, may be generic or equivocal. 122
5. Example.
6. Or analogical.
7. Every Effect has a commensurate Cause.
8. The proximate Cause is the definition of the Effect.
9. Subjects which receive the same effect from dif-
ferent causes are specifically different.
* See Errata.
xvi CONTENTS.
Pass
§ 10. All the intermediates between a subject and its
attribute are causes.
11. But the proximate intermediate is the cause to the
subject.
Chap. XV.* The Okgan oi' Pkimaey Tkttths 126
§ 1. What is the mode and faculty of apprehending
immediate truths ?
2. The organ by which they are apprehended is not
originally perfect, but must be developed by an
inferior power.
3. This power is Sense.
4. The process of development is Generalization.
5. The organ of immediate truths must be superior
to Science, and therefore is Reason.
APPENDIX A.
AXIOMS 131
§ 1. Forms of the Axiom.
2. Opponents of the Axioms.
3. Science that discusses the Axioms.
4. Defence of the Axioms.
5. Function of Ijhe Axioms.
6. Ubiquity of the Axioms.
7. Relation of the Axioms to Metaphysics and Logic.
APPENDIX B.
HYPOTHESES 139
§ 1. An Hypothesis is a peculiar principle affirming
the existence of an ultimate Cause.
2. It is defective in evidence.
3. Consequences of this character.
4. Art is Hypothetical.
5. Relative Hypothesis.
6. The Collocation of permanent causes is asserted
in the Hypothesis. •
* See Errata.
INTRODUCTION.
SKETCH OF THE ORGANON.
§ 1. In every Science may be found some general problem,
to the complete solution of which all its inquiries converge; some
central idea that unites all its members in an organic whole,
however great their variety. It is by the Idea alone that we
can determine into how many branches an inquiry should be
divided, and what is the relative importance of these branches;
what investigation is essential to the science, and what is nuga-
tory or extraneous.
The development of a particular Idea, curiosity to solve a par-
ticular problem, is not a matter of accident in the history of in-
dividuals or of nations. At one period the possession of a
science becomes a want, its problems force themselves on the
mind, and are importunate in their demands for a solution. At
other times and under other circumstances the interest may be
unfelt, and it may be almost impossible even to conceive the
problem. This may be seen in the history of Theology, Philo-
sophy, Political Science, Political Economy. In times unpropi-
tious to a given study, a great and perhaps insoluble difficulty
will be to determine what end it proposes, and what is its proper
province. In more propitious times its questions will present
themselves unbidden, and its old doctrines, if forgotten, will be re-
discovered. This has been exemplified in the history of Logic.
Its problem, the Conditions of Science, can only be a matter of
curiosity to a scientific age : that is, either an age that actually
B
2 MODERN WRITERS.
possesses many sciences ; or an age that is strongly possessed by
the Idea, and feels a restless aspiration to reduce it to a reality.
The Logical problem at a certain period forced itself on the
Greeks: it was attempted by Parmenides and others, and re-
ceiyed a provisional solution at the hands of Plato and Aristotle.
Some time had to elapse before the inadequacy of this solution
could be felt: for a time the interest ceased; the idea was no
longer a portion of the world's thought: if the old treatises
existed, the life that once animated them was extinct; and from
yarious causes men did not begin to demand a revision of the old
solution till about the time of Bacon. Educated Europe then
felt the same want that had been felt by Aristotle and Parmeni-
des ; and the New Organon was produced by the same idea, by
the same desire, that had before produced the Old. The men of
one age, however, are not all moulded by the same influences, and
there are numerous writers since this time whose treatises have
not much beside their name in common with the works t)f Aristotle
or Bacon. Not that there is any want of writers, who, with Bacon,
felt the necessity of determining the Method of scientific inquiry;
or who, living later, when so many sciences had been actually
constructed, and thereby so many new and glorious phaeno-
mena introduced into the world, were desirous to study the laws
of these phsenomena, and to trace the processes by which they
had arisen.
That the reader may understand the nature of the following
work, an account should be premised of the scope and drift of
the general inquiry of which it forms a part. What this is has
already been briefly intimated; but that the reader may become
more familiarized with the conception, it may be expedient not
to dismiss the question at once ; and as Aristotle's works are
I incomplete and contain no such plan or deflnition, we may take a
j rapid survey of some of the independent writers on the same
I subject in modern times, whose view of the problem is essentially
the same, however they may difiier in its treatment. Hereby we
shall gain the authority of their names for the view we take, and,
by noticing any questions which some of them may have handled
and others neglected, may have an opportunity of bringing out
into relief the main branches into which the inquiry is subdivided.
§ 2. In the Introduction to his System of Logic, Mr. Mill
MILL. 3
announces that he is going to expound the Science of Evidence;
and points out the limits that divide it from Metaphysics. Logic,
according to his view, is not the science of Belief, but of Belief so
far as it professes to be founded upon Proof. To determine what
facts are ultimate, and what are resolvable into others, what are
the propositions for the establishment of which Evidence is not re-
quired, is the office not of Logic, but of the sister science of Me-
taphysics. His definition is unobjectionable; but his limitation,
which is adopted to avoid certain matters of controversy, appears
to be erroneous. Relatives and Opposites, if we may be allowed
to assume an Aristotelian maxim, fall under the same science :
the scientific explanation of one Relative or Opposite is at the
same time an explanation of its correlative. Now derivative
truths and nnderived truths, concluded and unconcluded, pri-
mary and secondary, are both Opposites and Correlatives, the
one being the evidence and ultimate ground of the other. Logic
then, if we admit the soundness of this principle, as it treats off
the former, must also treat of the latter; as it treats of the nature
of conclusions, must also treat of the nature of original premisses.
Again, it is a reasonable maxim i that the same theory should i
treat of the whole of a class. If then Logic examines Science,
it must not separate it into two parts, examine the one and ne-
glect the other, examine the superstructure, and neglect the basis
or foundation. In other words, the same science which treats
of one Criterion or truth-organ, must treat of all the Criteria or
truth-organs : that which investigates the faculty of Inferences ,
must also investigate the faculty of Intuitions: that which/
examines the instrument of Mediate must examine the instrument
of Immediate truth-apprehension. Or, to use Mr. MUl's own|
term, the science of Evidence must not content itself with exa-!
mining the nature of derivative or borrowed evidence, but must
also ascertain the conditions of underived or unborrowed
evidence.
Mr. Mill allows that Logic and Metaphysics, according to his
conception of them, will form the two halves of one whole body
of truth; but his practice shows a closer connexion between them ;|
than he allows in theory. His own treatise is an instance of the
' Post. Anal. I. 28.
4 MODERN WRITERS.
limpossibility of going far into the conditions of Inference with-
out entering into the question of truths unsusceptible of inference:
for though he seems to have intended to avoid the topic, and in-
deed announces that his theory will be such as the disciples of
Hartley and Reid, of Locke and Kant, can equally accept; yet
the topic is broached, and he himself clearly appears as an ad-
herent of what is called the Sensational school.
In Mr. Whewell's Philosophy of the Inductive Sciences the
nature of Logic is described with great precision. It is a com-
plete insight into the essence and conditions of all real know-
ledge, and an exposition of the best methods for the discovery
of new truths. Its province is to determine the difference be-
tween true knowledge and its precarious or illusory semblances,
and the conditions under which it is obtained. Still shorter, it
is the theory which explains the nature of knowledge, and the
process of discovery. These definitions are not so general as
that given by Mr. Mill, which proposes for discussion all evidence
whether scientific or unscientific ; nor do they profess to apply
to more than one branch of Logic. Another branch investigates
the conditions of legitimate and illegitimate Opinion, i Yet, as
the highest element of an object chiefiy constitutes its essence,
and should be given in its definition, and the investigation of
Science is of higher rank and value than the investigation of
Opinion, the above formulae would not be inadmissible as
definitions of the whole genus. Logic.
The discrimination between Scientific and Unscientific methpd
has ever been the leading aim and inspiration of the genuine
logician. We have traces of this antithesis in the fragments of
Parmenides where he compares Reason and Opinion; in the Pla-
tonic contrast of Dialectical and Rhetorical reasoning ; and Ari-
stotle's distinctions between Science and Dialectics. The writers
hardly deserve the name of logicians who confine themselves to
examining the conditions of all reasoning, that is, the laws which
are common both to Scientific and Unscientific or Dialectical me-
thod, without going on to the inquiry to which this is merely
' 'Ekouttov yap to ptXnaTov iv ry — ^Topics vi. 12.
ovaiij. fiaKiara, .... fiore tovto leal 'PtiHov oiv ij j-4 fSeXTurrov rj to
Tov bpiaiibv tSn fiaXkov Bi\jiiaivtiv. laxarov. — Topics vi. 8.
WHEWELL, BACON, KANT. 5
preparatory, what are the peculiarities which constitute the
superiority of the former.
This inquiry is the end proposed by the author of the Novum
Organum. We have here indeed but the undeveloped germ, the
rudimentary idea of the new method : but it is the idea, the germ,
in its full vigour and power, safe to strike deep root in all minds
fitted to receive it, and realize its mighty destiny. It may be
doubted whether the spirit of the method may not even now be
better caijght from the original work of Bacon, rough and inarti-
cvdate as it is, than from the more finished treatises that have ap-
peared after the instrument had been perfected and polished by
practice. This work is an instance how much less a degree of
precision is required for practical purposes than is demanded in
speculation. It cannot be disputed, that, by acting on men like
Newton, Bacon was to a certain degree the creator of the modem
sciences. Yet how little is there in his works but the reiterated
doctrine, a thousand ways illustrated and enforced, that if any
thing like science was to be obtained, the preliminary observa-
tions must be more exact, and more numerous ! That which
chiefly displays the greatness of Bacon's mind, and most im- ) ;
presses the reader with admiration, is the strong faith he places
in the powers of the new method, and the almost prophetic insight 1 1
with which he hails the regeneration of the sciences that would
ensue. And yet there were plausible objections to be urged
against its success. There is printed among his works an in-
structive letter from a certain Thomas Bodley ; which might afibrd
consolation to any one who finds scepticism where he looks for
encouragement. Bodley, though in a friendly manner, attempts,
and that with great plausibility, to throw cold water on Bacon's
hopes ; giving him credit for ingenuity, &c., but quoting old pro-
verbs to the efiect that there is nothing new under the sun, and
insinuating that there was nothing new in his method; that, if
difierent, at most it was but different in degree : that philosophic
creeds were- destined to revolve, and that he was now merely re-
viving what had long ago been exploded: that before Bacon
many ardent enthusiasts had arisen, who had hoped by more per-
fect methods to increase the store of human knowledge, whose
attempts had proved abortive, &c. &c. This was from a person
whose judgment he respected. But he felt that the difference of
6 MODERN WRITERS.
degree was a difference of kind, and continued to urge the world
to adopt the new plan, and time has verified his anticipations.
[ The Critic of Pure Reason, or Transcendental Logic, of Kant
;;' interests us so far as it is engaged with the same problem of ex-
' hibiting the structure of science: so far as it calls in question our
knowledge of a spiritual world, it is beside our purpose. He
divides the truths that compose the body of science into two
classes : material truths that are derived from experience ; and
those of a formative and organizing character, that are furnished
a priori by the mind. The object of the Critic is to specify the
latter, and the progress of the discussion discloses his views of
; the constitution of philosophy. He divides formal principles
, into four classes, as contributed by Sense, Understanding, Judg-
' ment, and Reason. The pure or a priori Sense supplies the per-
ception of Space and Time, creating the mathematical sciences,
whose laws penetrate the future structure of truth in all directions.
The Understanding furnishes certain generic conceptions and
axioms, under which experiences must fall, and by which they
must be governed.
The Judgment, in what he calls its Reflective office, gives the
precept of Generalization, or the command to look for Unity in
Plurality, with the expectation of ultimately completing the pro-
cess. In its Determining faculty it issues the precept of Specifi-
cation, or the command to look for Plurality in Unity, whether
in dividing and particularizing the above-named axioms and
conceptions of the Understanding, or in subdividing the orders
and laws discovered by Induction.
^ ' The Speculative Reason furnishes certain supreme Ideas, ne-
cessary to complete the systematizing process, and to cement the
whole of thought together in absolute unity.
Practical Reason, besides supplying to Speculation its supreme
Idea, creates itself the whole science of Morality.
Thus we hare the outline and framework of the whole of
philosophy, and of one portion of it something more. The re-
mainder, the materials to fill up this outline, to fit into this frame-
work, must be supplied by Sense and Induction. We see, then,
that the purpose of Kant, as well as of the above-mentioned
writers, was to exhibit the outlines and lineaments o^ Philosophy.
We might quote others who have been engaged on the same
PROBLEMS OF LOGIC. 7
subject, but that we have ali-eady quoted enough. As these j
writers have been adduced to throw light on the views of Ari- ,'
stotle, we may further compare them on certain points suggested
by his writings.
We shall find that one problem of his Logic is the determina-
tion of the formative truths or Axioms; or principles indepen-
dent of Experience, and common to all the sciences. (A.)
Another problem is the nature of the Theses, or principles »
characteristic of their appropriate science ; their relation to the
conclusions ; and the shape and constitution of the whole body
of truth in which they are incorporated. (B.)
A third problem is the method of Induction, or the process by >■
which principles are discovered. (C.)
Kant's Critic of Pure Reason discusses A, which is indeed its
great object; throws light incidentally on B; and omits C, which
is foreign to his plan.
It did not belong to Bacon to recognize A ; he will not antici-
pate a very definite solution of B ; and is chiefly employed on C
Mr. WheweU treats of B and C, and apparently of A ; but it
is not clear where he draws the line between a priori and a pos-
teriori conceptions : his Axioms are not similar to those of Ari-
stotle, and contain what is characteristic of particidar sciences.
Mr. Mill investigates B and C, but does not recognize A ; al-
though he seems unsuccessful in explaining the principle of Uni-
formity by Experience, and his account of the Canons of Induc-
tion assumes the principle of Causation.
By this time it may be hoped that we have a tolerably clear
conception of a certain subject matter which many writers have
considered worthy of scientific investigation. To give however I
such a definition of Logic as shall clearly show the limits that /
part it from Metaphysics, is by no means easy. If, for instance,
Logic is the science of Knowledge, there are some questions
about Knowledge which Logic does not consider. The relation '
of Subject and Object, of the Mind and the World, of our con-
ceptions of the world, and that which the world is in itself inde-
pendently of our conceptions, are questions which must be as-
signed to Metaphysics. Th? se may be excluded, by ascribing to
Logic the theory of the internal, not the external relations of
Knowledge. What is the final shape and organization of human
8 CONTENTS OF THE ORGANON.
/ Belief, what the relation of affiliation or interdependency between
\ two portions of thought, whatever may be their relation to out-
ward existences, will then constitute the problems of Logic.
§ 3. We may next give a rapid sketch of the contents of the
Organon, in order to render more intelligible that portion of it
which is here translated. If we assume that Logic has to deter-
j mine what is the perfection of the intellectual faculties, and what
are the measures to be taken for this end, it wUl inquire what is
the nature of Science, and how it is to be pursued ; and what is
Opinion, for this is often the utmost we can obtain, and how se-
' curable, as far as may be, from error. The formation of Science
and of Opinion, by which we mean any unscientific belief, is
partly similar, partly dissimilar. Logic, then, will naturally fall
' into three di^'isions : —
I (A.) The generic branch, which treats of reasoning in general,
i whether the result is Opinion or Science.
(B.) The specific branch, which treats of reasoning the result
of which is Science, Inductive or Deductive.
(C.) The specific branch, which treats of Dialectical reasoning,
the result of which is Opinion.
(A.) This branch is contained in the Prior Analytics, to which
we may append the Hermenia and Categories. The first of these
treats of Syllogism, the second of Propositions, the third of
Terms. Their contents are well known, having been transfused
into the works of the scholastic logicians, whose only fault was
that they did not sufficiently perceive that these were merely
preliminary inquiries. The principle involved in all Syllogism
is the dictum de omni et nullo^ which it will appear is identical
with the Axiom, or the principle of Contradiction. When
Dugald Stewart observes that the whole of the science of Syllo-
gism is comprised or implied in the terms of one single Axiom,
his assertion is quite correct ; the doctrine of Syllogism merely
determining, on the authority of the Axiom itself, under what
conditions the Axiom is applicable.
His assertion, however, (Philosophy of the Human Mind,
part 2, chapter 3,) that the object of Aristotle is to demonstrate
by abstract reasoning the conclusiveness of demonstration, to
' See Appendix, (A.)
MODALITY. 9
demonstrate by the syllogistic theory the validity of the syllo-
gistic theory, is totally unfounded. No doctrine is enforced
with more emphasis by Aristotle than this, that some truths are
indemonstrable : and the very proposition he instances as being
plainly indemonstrable, both as possessing already the highest
possible evidence, and as required for the demonstration of other
truths, is the A:xiom or principle of Syllogism.' To show the
limits of its application, he employs the principle itself, because
it is supreme, and there was no higher authority to which he
could appeal.
The laws of Modality are investigated in an inquiry that
is preliminary to the theory of Science, as a certain modality
of premisses and conclusions is an essential characteristic of
science. Modality is sometimes called Matter, and it is a com- \
mon doctrine that matter is extralogical, and this would seem j
to exclude modality from the consideration of Logic. Now the
expression, that matter is extralogical, may mean, that, though
Logic examines Science, Astronomy for instance, yet it teaches
nothing about the stars, the subject-matter of Astronomy.
For every science has its own subject-matter or province with
which no other science interferes. But though Logic teaches
nothing about the matter of Astronomy, yet, as a science, Logic
has its own subject-matter, to which Astronomy is equally a
stranger. So the matter of Chemistry is extralogical, and the
matter of Logic is extrachemical. However, it is too evident a f
fallacy to infer, that because the matter (of other sciences) is \
extralogical, therefore Modality, sometimes called Matter, is !
extralogical. But it may perhaps be urged, that none but the
professor of a particidar science can know the modality of a par-
ticular proposition ; and therefore it cannot be treated of by
Logic. But Logic is equally ignorant of the quantity and quality
of the proposition arising from the connection of two terms, and
yet it investigates the laws of quantity and quality: it will
therefore investigate Modality as it does quantity and quality,
that is, hypothetically.
If the words Matter and Form are used in the Kantian sense,
then it must be remembered that the notions of necessity and
' See Appendix, (a.)
C
10 CONTENTS OF THE ORGANON.
contingency compose, according to Kant, part of the formal
furniture of the mind, and in this view Modality would fall
under the province of Logic.
i Another subject discussed in the Prior Analytics is the fact,
[that false premisses may give a true conclusion, i. e. that an
hypothesis is not sufficiently established by showing that its con-
sequences agree with phsenomena : and the mode in which pre-
misses and conclusions may reciprocate : inquiries which seem
to be a preparation for explaining the nature of Analytical and
Synthetical reasoning, i and the method of testing Hypotheses.
Also a slight and inadequate account of Induction is given. In
general it must be confessed of these treatises, that the investi-
gations are carried out with a minuteness that may be curious,
but is not otherwise either interesting or valuable.
§ 4. Having concluded the generic theory of Syllogism, we
proceed to its specific peculiarities.
B. We treat at first of Deductive Science : and this division
leads us naturally to inquire, to which class does Logic itself
belong, Deductive or Inductive ? Aristotle treats it deductively,
for he begins ^^ by defining Science to be the teference of the
laws of phsenomena to their causes. We must not suppose
I however that he was entitled to assume a definition, as in the
I simplest mathematical sciences, without any justificatory inquiry.
Logic, like Politics, is a practical science ; its reasoning is Ana-
lytical, and the basis of its reasoning the conception of an end
to be attained. As the end of Politics is happiness, or some-
thing similar, and its problem the measures and machinery by
which it may be promoted ; so the end of Logic is science, and
,iits problem the process of discovery : and the justification of the
Iprinciple it assumes, that is, of the end it proposes, would ap-
pear to consist in the proof of two propositions : these proposi-
ti tions are : that no higher end is practicable, and that there is no
linsurmountable obstacle to the attainment bf the end proposed.
'When these are proved, we may assume that the end is rightly
selected, and that the theory rests on its appropriate basis.
' For an explanation of these pro- Bophy of the Human Mind, part ii.
cesses see Dugald Stewart's Philo- chap. 4. ' Post. Anal. i. 2.
SCIENCE INVESTIGATES CAUSES. 11
Now with regard to the former point, there are none who
maintain that the aim selected is not sufficiently high : for the
dissentient school contends that it is only too ambitious, insist-
ing that science must renounce the hope of discovering Causes,
and content itself with a humbler aim, the knowledge of Laws.
The legitimacy of the hypothesis then depends on the otherj
point, the truth of the suppositions analytically involved, or the'
feasibility of the steps demanded : what these are we shall pre-
sently examine.
Meantime it .must be observed, that the main characteristic of j
Aristotle's Logic, which is both the foundation of the rest of his '
own theory, and brings him into contrast with a modern school,
is his attributing to science the investigation of Causes. Many
writers — ^for instance, Hobbes, Berkeley, Hume, Brown, Dugald
Stewart, Comte — deny the existence of any thing like causation,
maintaining that what is so called is merely the invariable, but, f
for all we know, arbitrary, conjunction of antecedent and conse-
quent. The maintainers of this theory confess that the belief in
natural causation is an universal instinct, which has been the
great impulse to scientific research. They seem to have for-
gotten the mathematical sciences ; for no one could maintain
that the attributes of figure and number — for instance, that the
interior angles of a triangle are equal to two right angles, or
that three is the cube root of twenty-seven — are merely arbitrary
and fatal ; and it has not been shown why physical cause and
effect are not as naturally connected as mathematical subjects
and attributes.^
To abandon the notion of Causation is to abandon the notion
of Necessity as a characteristic of knowledge : for however con-
stant and fatal the conj unction of two terms may be, yet if we only
perceive them in juxtaposition, unless we perceive the manner
in which they are locked and linked together by their essences,
we cannot recognize the necessity of their connection.
If however we introduce the notion of Causation and intelli-
gible Necessity,* we are inevitably led to rest science on defini-
tions : for in order to perceive the essential interpenetration 6f
' See Whewell, PhUosophy of the book xi. 16.
Inductive Sciences, book iii., also ' Post. Anal, book i. 4, 6.
v^
12 SCIENTIFIC PRINCIPLES.
any two terms, we must have a distinct conception of their
essence, and the expression of such a conception is Definition.
From this consideration some characteristics of scientific pro-
positions might be deduced, which will be found to distinguish
them from dialectical propositions. The terms of a scientific
proposition, being essentially connected, will be coextensive or
commensurate. ' Again, if the diversity of sciences depends on
the diversity of the genus investigated, and Nature is heteroge-
neous, there will be a multiplicity of sciences ; ^ and as the same
predicate cannot be homogeneous to two heterogeneous subjects,
the same predicate will not enter two difiierent sciences, but
every scientific proposition will be confined to its one appropriate
science. Whilst these are necessary, essential, coextensive,
appropriate; dialectical predicates and propositions are contin-
gent, accidental, incommensurate, and promiscuous or indeter-
minate.
If the conclusions of science must satisfy these conditions, it
is not difiicult to see what must be the nature of its foundations.
(1.) Definitions wiU be required, both of subject and of attri-
bute, both of the compound and of the elementary. 3 The defi-
nition of the elementary will not be further analyzable ; the
definition of the compound and dependent must contain its
elements and antecedents : and thus its parts will correspond to
the premisses and conclusions of a syllogism.
(2.) But we need more than Definitions : if we have merely
these, our conclusion will be merely hypothetical. To give it a
categorical character, we must be able to assert the real existence
of the subject in which the attribute inheres, or of the primary
power or elementary substance which generates the remote con-
sequence. The proposition containing this assertion is called
the Hypothesis.
(3.) If we are not sensible of wanting more than these, still
there is another principle which we always tacitly assume. In
passing from any premisses to a conclusion, we rest upon the
Axiom, or the principle of syllogism. The intuition of this
principle constitutes the reasoning faculty. It is not always
■ Post. Anal, book i. 4, 5. ' Post. Anal, book i. 7, 9, '27, 32.
' Post. Anal. ii. 8.
THERE MUST BE FIRST CAUSES. 13
used in its widest extent, in which it is a predication of identity:
in mathematics it is merely regarded as a predication of equality.
The Topics of Dialectics and Rhetoric are mostly particular cases
of the Axiom.
These elements of knowledge, which form the basis of Deduc-
tive science, will form the conclusions of Inductive inquiry: ifor
in general the problems of all sciences may be divided into
four classes : —
(1.) Is it a fact, that a given subject possesses a given attri-
bute?
(2.) What is the reason of the fact, that a given subject pos-
sesses a given attribute ?
(3.) Is a given conception of an elementary substance or
power imaginary, or real ?
(4.) "What is the character of a certain primary substance or
power ?
Of these the third and fourth are Hypothesis and Definition,
the result of Inductive inquiry, and the basis of Deduction.
The second problem should be answered by Demonstration, and
its answer will contain the solution of the first.
We may now consider the question suggested above, what
suppositions are involved analytically in the hypothesis, in the
possibility of science such as we defined. They are two : the
one may be called an ontological, the other a psychological pos-
tulate. As science ^ professes to explain causes and answer
every Why ?, the series of genera and difierentiee that enter into
the composition of an object must be finite, for the cause of a
generic property is to be found in the definition of the genus ;
and there would be no exhausting the series of possible ques-
tions, why a subject possesses a given generic property, unless
the number of genera and difierentiae contained in the subject is
finite. And as the series composing the formal cause of a sub-
ject must come to an end, in order that we may reach the formal
element that is immediately connected with the predicate ; so
must the series of material, efiicient, and final causation come
to an end, in order that we may exhaust the questions Why?,
when the immediate antecedent happens to be a term in the
' Post. Anal. ii. 1. ' Post. Anal. i. 19, 20, 21, 22.
14 THERE MUST BE AN INTUITIVE FACULTY.
material, efficient, or final series. On these suppositions de-
pends the possibility of realizing the scientific idea. Unless we
have first Causes, and unless the series of Generalization is finite,
we have no basis of Demonstration. Both of these suppositions
— that the chain of antecedent causes to any consequent, and the
number of specific elements in any essence, are finite — are ex-
pressed by Aristotle in the assumption, that every object is
definable, for the definition includes every kind of cause ; and this
may be called an Ontological hypothesis.
This supposition however thai; there are indemonstrable truths
is not alone sufficient to show the possibility of Demonstration:
we must further assume that we have some faculty or faculties
corresponding to these truths, and capable of apprehending
them : Aristotle asserts* that Sense and Reason are such facul-
ties : and this may be called a Psychological hypothesis. These
two hypotheses, then, are indispensable to the theory of science.
Let us first consider the Psychological hypothesis.
Upon this subject bear the controversies about the Criterion or
Organ of truth. Philosophers were divided into those who
denied and those who maintained the existence of a Criterion :
the former were the Sceptics. Those who maintained a Crite-
rion either advocated a simple or a mixed Criterion : the ad-
vocates of the former were divided into Sensationalists and
Rationalists, as they advocated Sense or Reason ; the advocates
of the latter accepted both Sense and Reason. Democritus and
Leuoippus were Sensationalists : Parmenides and the Pytha-
goreans were Rationalists : Plato and Aristotle belonged to the
mixed school. Among those who advocated Reason as a Crite-
rion there was an important difierence : some advocating the
common Reason, as Heraclitus and Anaxagoras: others the
scientific Reason, or the Reason as cultivated and developed by
education, as Parmenides, the Pythagoreans, Plato and Aristotle.
In the Republic, 2 Plato prescribes a training calculated to prepare
the Reason for the perception of higher truths. Aristotle re-
quires education for the Moral Reason. The older Greeks used
' Post. Anal. i. 3, and ii. 15. Baiperai Tt xal dvaZuirvpurai. — De
^ EV TovToig Totg iiadrj/iaaiv Hepublica, vii. § 9.
£(caffrot£ opyavov n ^vxve kKxa-
THERE MUST BE AN INTUITIVE FACULTY. 15
the word Measure instead of Criterion : and Protagoras had said
that Man was the Measure of all truth. This Aristotle interprets
to mean that Sense and Reason are the organs of truth ; i and he
accepts the doctrine, if limited to these faculties in a healthy and
perfect condition. These names then cannot properly be ranked
among the Common Sense philosophers, where they are placed
by Sir WiUiam Hamilton.
The manner in which the WiU is the Criterion of moral truth
may be left to the theory of Morality. It is where the faculty
has to be trained before it is Capable of perception, as in the
fine arts and morals, that the theory of the Criterion is most
difficult, and it is here that the Sceptics find it most advan-
tageous to maintain the controversy. There is nothing on the
subject in the Organon.
When Reason is said to be an Organ of truth, we must include,
besides the intuitive, the syllogistic faculty. This is the in-
strument of the mediate or indirect apprehension of truth, as the
other of immediate. The examination of these instruments, in
order to discover their capabilities and right use, is Logic.
This appears to be the reason why Aristotle gave the title of
Organon to his Logic. So Epicurus called his the Canon or
Criterion. The controversy on the Criterion is to be found at
length in Sextus Empiricus De Criterio.
What we have denominated the Ontological hypothesis ofi
Deductive Logic, the finiteness of generalization, appears to be ;
the same as the hypothesis demanded by General Logic, the
existence of universals, and the hypothesis of Inductive Logic,
the uniformity of nature. General Logic demands the exist-
ence of universals*: for though it would be possible to reason,
as Aristotle observes, without the Platonic Ideas, it would not
without universals ; for without these there could be no middle
term (which is always universal), and without a middle term no
syllogism. Inductive Logic also makes a similar hypothesis,
imder the name of the Inductive principle, the belief that Na-
ture is a " tissue of laws," or that she is " stable and uniform."
These hypotheses, which are necessary for Syllogism and In-
duction, do not appear essentially distinct from the hypothesis
• Metaph. x. 2, and xi; 6. ' Post. Anal. i. II.
16 THERE MUST BE FIRST CAUSES.
■which is necessary for Demonstration. For the same tendency
that made us reduce the number of particulars by ranging them
under universals would impel us to reduce those universals by
ranging them under others still higher ; and the simplifying
process, which began by reducing the Infinite to the Many,
■would not desist tiU it had reduced the Many to the One,
Besides the existence of universals, Deductive Logic makes
the hypothesis that every event has a cause, and that the chain
of causation is finite. As, however, the reduction of univer-
sals to the one appeared the work of the same principle that
reduced the infinite to universals, and was not the matter of a
distinct postulate, so the principle of looking for an absolute
primary may be considered the same as that of looking for an
antecedent, and does not require a separate hypothesis.
The principle of the finiteness of the chains of generalization
and causation belongs to the science of Being. In the Orga-
non the argument is led so far, and then dropped. The prin-
ciple is asserted and briefly considered in the Metaphysics, i
[■ These hypotheses of Deductive Logic — the necessity of
I assuming an absolute termination to the generalizing series, and
an absolute beginning to the chain of antecedent and consequent,
if science is to be possible — are recognized by Kant, and ascribed
to the Reflective Judgment and Reason. The fact that laws
can thus be given to Nature by the mind, he calls its autonomy
or legislative power. He connects the law of Generalization
and Specification with the teleological principle, by which we
introduce final causes into natural science. As the organization
of objects is determined by their end or destiny, so, if the end of
Nature is to be known, she will obey any laws which are the
conditions of being known : and as the condition of her com-
prehensibility is the finiteness of the above-mentioned processes,
it follows that these processes are finite.
§ 5. The Inductive method shall be considered after we have
discussed the nature of Dialectics.
(C.) Dialectics is defined^ to be the method of arguing with
' Metaph. ii. 2. avroi \6yov VTrixovrcg fi^Oiv ipov-
^ MI9o Joe d0' riQ SvvtiaofuBa av\- jiev virtvavTwv. — Topics, i. 1 . A
\oyiZ,i<sdai irtpl iravTog tov Trpore- similar definition is given Soph.
OevTog vpojiXriiJiaTog I? ivioliav, sal Elench. 34, where it is called a
DIALECTICS OF PLATO. 17
probability on any given problem, and of defending a tenet
■without inconsistency.
We cannot always, for instance in the practical aflFairs of life,
argue with scientific rigour, and even the scientific method by
which we discover principles must differ from that by which we
develope their consequences. Besides then the doctrine of De-
monstration and of Scientific Induction, we require a theory to
' unfold all the possible kinds of argumentation and less rigorous
methods of fortifying an opinion.
The Aristotelian Dialectics must be distinguished from the
Dialectics of Plato, who included under this name his Metaphy-
sics or Philosophy, as well as the Aristotelian Dialectics. Now.
his Philosophy was a determinate science with a determinate!
province, whereas the latter is unscientific reasoning in any pro- '
vince whatsoever. It was very natural, however, to call them by
the same name. Dialectics, as we shall see, or something like
it, must always be employed by sciences that have to establish
their first principles ; for its great function is to examine hypo-
theses, and test their legitimacy by deduction of their conse-
quences. In this respect it presents an antithesis to the Mathe-
matical sciences, which rest on given principles, and have only to
unfold them: and this is the function that, in speaking of Dia-
lectics, Plato generally has in his eye. Philosophy presents the
same contrast to the Deductive sciences ; for at its outset it has
no definite principles, and to fix them must employ a Dialectical
method. There is a greater air of liberty and independence about
both Dialectics and Philosophy: the sciences have their task im-
posed them: certain principles are rigorously prescribed from
which they must not depart : whereas the ofiice of Dialectics and
Philosophy is the determination of principles ; and every thing
is subject to their criticism. Both too have an air of univer-
sality: for Philosophy, considering the supreme sources of the
systematic unity of nature, contemplates to a certain degree the
provinces of all the sciences : and Dialectics is not, like science,
divided into branches, but is opinionative argumentation in all
Faculty ; in another place ■ it is Ky nupaarucbi SuAcktikoc. — Soph,
called an Art, o rexvy avKkoyiari- Elench. 11.
18 LOGIC OF OPINION.
provinces indiscriminately; a fact, Aristotle observes,' that ac-
counts for their confusion. Besides using Dialectics as a name
for Philosophy, Plato as well as Aristotle applied it to any rea-
soning not founded on scientific principles.
As the ancients confounded it with Metaphysics, so in modern
times it has been confounded with Logic. The popular notion
of the latter, prevalent among the lay public, though not per-
haps among professed logicians, exactly corresponds to the na-
ture of Dialectics. It therefore may be worth while to point out
their relation. Dialectics, like Science, is not Logic, but the sub-
ject-matter of Logic. Logic considers Astronomy, but is not As-
tronomy, and similarly she contemplates Dialectics, but is not
Dialectics. The stars are the subject-matter of Astronomy, and
the animal kingdom of Zoology: but the stars are not Astronomy,
nor are animals Zoology. So Dialectics is a subject-matter of
Logic ; is handled, anatomized, and its conditions determined by
Logic ; but for all that it is not Logic, any more than the animal
ikingdom is Zoology, or the vegetable kingdom is Botany. If
iDialectics is Logic, then Ethics is Logic, and Chemistry is Logic ;
for there is the same relation between Logic and Dialectics that
there is between Logic and Science.
It must be observed, however, that as Science is chiefly cha-
racterized, by its peculiar propositions or Theses, while the com-
mon principles are unimportant; so Dialectics is characterized
by its common or topical propositions, all of which may apply to
any one subject, and any one of which may apply to all subjects ;
(for which reason there is but one Dialectics, while there are many
sciences :) from which it follows, that the Logic of Dialectics, which
enumerates these topics, will go further to constitute the dialec-
tician, than the Logic of Science, which cannot enumerate the
Theses, to confer the possession of a particular science. ^ In this
' TO airb viroBvovTai a%rijia Tif wg tivavTog ttiq SiaKeKTiKrjs iariv
ipi\oa6^(f TTipi /lev yelp to avrb yi- ISeXv, tj avTfJQ 'o\t]g fj ftkaove rivog.
voQ <TTps(peTai ri diaXeKTiK'^ Ty 0t\o- — Rhet. i. 1. Here Dialectics itself
aofiif iaTi Si ri SiaXiKTiKr) ntipa- is said to theorize {iSiiv), and General
(TTiK^ irepl S>v ■>) 0i\o(7o0ia yvdipia- Logic seems to be called a part of
TiKT]. — Metaph. iv. 2. Dialectics. This latter statement
" This may explain the passage in must be inaccurate : for General
the Rhetoric, Trepf ovKKoyLa/tov o/ioi- Logic is a preliminary to the theory
CONTRAST OF DIALECTICS AND SCIENCE. 19
light the theory of Dialectics may be considered to be an inte-
gral part of Dialectics: and thus it happens that, though Dia-
lectics and Logic are related as Logic and Science, yet there is
a closer connection between the former than between the latter.
At the risk of creating confusion, we must notice that the word
Logic, as applied to the Science of Evidence, and as we have
hitherto used it, is modern. Aristotle's term for this theory is
Analytical Science.^ When he uses the word Logical, he uses it
as equivalent to Dialectical; and he generally uses it when he
wishes to oppose the Dialectical to the Scientific. It, or some
cognate, will occur in several of the passages we shall proceed to
quote, but to avoid confusion we shall always translate it by the
word Dialectical.
(1.) An argument is Dialectical that rests on Inappropriate
principles, that pursues an Inappropriate method.
As in Physical science the Appropriate method is Inductive,
Dialectical is often opposed to Inductive.
Democritus reasoned inductively, and is instanced as using a
Physical and Appropriate, not a Dialectical, method. Others
were great dialecticians but no observers, and therefore unsuc-
cessful in their physical theories. Great familiarity with phae-
nomena is necessary for the Physical philosopher.^
The forced and strained theories of philosophers are due to
their perverse method. They make every thing bend to certain
assumed dogmas, instead of being guided by observation.*
The more abstract a Dialectical proof is, the wider it departs
from the Appropriate principles.*
of Science, jiist as much as to the ' tovtov S" ainov rb /irj KaXuJg
theory of Dialectics : but it is possi- Xa^uv r&g irpwraq apxitg, aWA.
ble that Dialectics is here not used navra ^ovXtaBai irpoQ nvag So^ag
in its proper sense, but as a synonym mpKr/iBvag civayeiv' Set yap icrbig
for Analytics or Logic. tSv jiiv aMrirdv aiaOr/TAg, tSiv
' Khet. i. 4 ; Anal. Post. i. 22. Si aiSiuv diSiovg, tS>v Si fQapT&v
" ISoi S' av Tig KoX Ik tovtiov '6aov (jSaprag Aval rhg apxcig, oXiag S"
Sia^kpovaiv ol (pvatieSig xai Xoyucfis ofioyeveig Tolg iiTroiceifiBvoig. — De
aKOTTOVvrag AriiioKpiTog 3" &v Coelo, iii. 7.
^avtii) oiKitoig (cat ^vaiKoXg Xoyoig * 'AiroSei^tg \oyiK^ . . . '6(T(f Ka96-
irfTriiadai. Neglect of Observation \ov nSXKov iroftpiorkpio tS>v oiKcioiv
is called Smipia. — De Gen. et apx<!>v. — De Gen. Anim. ii. 8.
Corp. i. 3.
20 LOGIC OF OPINION.
The theory of the Platonists arose from their Dialectical method,
for they were the first great dialecticians. i
Dialectical method is, however, not always opposed to Induc-
tion : it is applied to unscientific argument when the appropriate
principles are Deductive. There are two ^ examples of this in the
following treatise.
So far as a Dialectician or Rhetorician employs the appropriate
principles or appropriate method, he ceases to be a Dialectician,
and his argument becomes scientific.^
(2.) Another mode of expressing the peculiarity of Dialectics
as opposed to Science we have in the Rhetoric; that it has no
peculiar or appropriate subject genus.* Its arguments will apply
to heterogeneous subjects:* whereas no scientific proof can
migrate from its original science -fi for every science has a deter-
minate province, and, while there is but one Dialectics, there are
as many sciences as there are provinces. This property of
Dialectics is equivalent to the former, that it disregards the
Appropriate method.
(3.) Or we may characterize Dialectics by saying that its
treatment of any particular matter will be accidental,'' whereas
scientific .propositions are all essential to their subject-matter.^
This follows from the preceding: for any argument or medium
^ 7] tS)V hSCjv eltraytoyrf 5«i Trfv ov iripi ri ykvoQ i^iov aiphipicnk^
Iv toXq Xoymg eyevero ff/csi/ziv ol yap vov. — Rhet. i. 2.
npoTspoi AiaXcKTiKijg ov fisTtixov. — wepi tov SoBivrog. — Ibid.
Metaph. i. 6. ov ■Kovriau inpl oiSiv ysvog ifi-
' Anal. Post. i. 23, and 32. ippova. — Rhet. i. 4.
' dv yap ivTVXV "PX^'S oiiKen Trepi wavTiov. — Soph. EI. II. Trepi
AiaXEBj-iK^ oiiSi 'VtiTopiKfj aW ixti- irav yevog. — Ibid.
vr) iarai fig Ix^i Tag dpxdg. — Rhet. = Bi6 Kal iir' oKKtav e^apfiorrovaiv
i. 2. 01 XSyoi oil trvyyevdv. — Post. An.
Xriazrai T'fiv fvaiv avToiv afavi- i. 9.
aag Tif fura^aivtiv liriaKiva^iiiv tig Tcpbg ■KoXXoiig 'iari fiEreveyKtiv. —
tTnarrifiag vTroKUjikviiiv rivwv wpa^ Soph. El. II.
yfiariov dWa firj jadvov \6y<i>v. — ^ ovk tariv 15 aXXov yevovg /ura-
Rhet. i. 4. jSavTa Sei^ai. — Post. An. i. 7.
Kal fiaXXov airrofitvoi Kara, rpoirov oiiK strri fisrsveyKeXv Sid to sk twv
(Bard rfiv o'lKuav jiiOoSov (?) ) iicTa- iSiav ilvai dpx<Sv. — Soph. El. 1 1 .
^a'lvovmv k% aiiTotv. — Rhet. i. 2. "^ KaTd (TVfi(3e^ijK6g.
* OVK icTTiv ivog Tivog yivovg dipa)- ' Kaff aiiTO, Kar ovaiav Kai Kara
piojikvov. — Rhet. i. 1. to ilSog. — Post. An. i. 23.
CONTRAST OF DIALECTICS AND SCIENCE. 21
of proof essential to a subject would be commensurate with the
limits of the subject, and peculiar and appropriate to that deter-
minate genus. An accidental proof may be good Dialectically,
but if it claims to be Scientific, is Sophistical.^
These three propositions then express the nature of Dialec-
tics, and they may all be considered as identical : —
(1.) That it employs an inappropriate or unscientific method.
(2.) That it has no determinate matter, but employs considera-
tions equally applicable to heterogeneous subjects.
(3.) That its statements are not essential to the subject of
discussion, but accidental.
The uses of a method thus characterized are said* to be
three : —
(1.) As an intellectual exercise.
(2.) In the common intercourse of life : for if we would per-
suade men we must appeal to their own opinions and convictions.
(3.) As an organ of the inductive sciences, for the discovery
of Principles. To this last use we shall recur hereafter.
Its features are most distinct in the form Pirastike, to which
its terminology originally belongs ; and which we will therefore
consider.
Pirastike is the examination of the pretender to a science,
with a view to ascertaining his real knowledge, by one who
makes no similar pretensions.' We have celebrated examples
of this in the encounters of Socrates with the Sophists. Some
of these professed universal knowledge, and gave oracular
answers on any subject to all inquirers. Socrates would
extract a dogma from them, and after eliciting further explana-
tory or justificatory statements, would put all their assertions
together, and show that they were self-contradictory, or led to
some acknowledged error. It is said that he was as dangerous
to the incompetent statesmen of his age, as to its false teachers.
' kmaraaQai rbv ao^iarucbv rpo- irpoairoiovjitvov. — Soph. El. 11.
irov rbv Kara avfi^t^rjKoQ. — Post. fiv av Ixoi Kai jifi dSiig ng. —
An. i. 2. owTTw oJSev ci /irj rbv aofi- Ibid.
ariKov rpoTOV. — Post. An. i. 5. Sio irdvTtg Kal oi ihwrai rpoirov
2 Topics i. 2. TIV& xpSivTai Ty HeipatrnKy' wdvTig
'■> AiaXeKTUcri ng . . . v Sewpet oil -/dp f^xpt Tivbg iyxtipovnv dvaKpi-
rbv diora dWd rbv dyvoovvra Kai vuv Tovg ivayyiWoidvovg. — Ibid.
22 LOGIC OF OPINION.
If the examiner is himself ignorant of a science, by what
premisses can he expose the false pretensions of another who
professes to know the science ? i The propositions he employs
must be conclusions or dependent truths, which would be
known to one who was master of the science,'^ but which also
may be known to one who cannot deduce them from their ap-
propriate principles,' without which knowledge is unscientific.
The process was finally subjected to strict rules, chiefly
calculated to secure the division of labour, by confining one
party to the defensive, the other to the oflTensive, to avoid
confusion, and prevent the dispute from becoming interminable.
The Answerer, the person who maintained the defensive,
began by enouncing some dogma or Thesis * which he was
willing to defend. This Thesis must not be confounded with
the scientific principle ; though, as the first truths of a science
were submitted to a Dialectical examination before they were
recognized, the two meanings would often coincide.
It was the oifice of the Questioner to show that this Thesis
led to obviously false consequences, or could not be defended
without an inconsistency. For this purpose he had not the
licence of the Orator, who may argue triumphantly from as-
sumptions his adversary would never concede, and obtain invin-
cible data from unscrupulous witnesses, but was confined to
propositions allowed by his opponent, and extracted by ques-
tioning, which made the process a series of Questions and An-
swers. And the Question was to be such as could be answered
by a simple affirmative or negative.^ If obvious, the proposition
ought to be conceded ; if otherwise, the Questionefhad to adduce
examples and claim it inductively. ^ The Answerer was not
' Sivarai truXXoyiJeffSai ypevSog Si eiSsvai Trjv Tsxvriv, /j,^ dSoTa Sk
ayvoiav Tov SiSovroQ rbv \6yov . . . avdyKtj ayvouv. — Soph . El. 11.
tiiffre TTOicT SfiKov d dyvoei. — Soph. ■* Topics, i. 9.
El. 8. ' irpbg ijv tanv AiroKpiveaBai,
^ SK ruiv doKovvTuiv Tt^ anoKpt- valj rj ov, — Topics, viii. 2.
vofiiv<j> Kai dvayKaiav uSkvai T<f TTpbg ^j/ r) airoKpiaig ri Kara^i)-
irpoaTroiovixivif 'ix'^iv Tr)v imaTr)- aavTi fj cLTrcxptjaavTi. — Ibid.
Iiii)v. — Soph. El. 3. ^ SiaXiKTigsfi yap kan Trporaaig
' SiStitmv oi)K Ik tS)V iSitov iW jrpbg iqv, o^Tutg im iroWdv tvov-
iK ruiv ETTouBviov, oaa Toiavrd ka- aav, /iri ianv 'ivaraaiQ. — Ibid.
Tiv d dSora jiiv oviiv kwXvh fiij
PIRASTIKE. 23
justified in denying it unless he adduced an Enstasis, or at least
an Antisyllogism. When the Questioner considered he had
sufficient premisses, he arranged them so as to show that they
contained an Elenchus.i or refutation of his adversary's position.
An Elenchus was considered meritorious if all its premisses
were highly probable, and also the thesis it destroyed:'' or if its
premisses and the thesis were all equally probable, for then there
would be no clue to discovering the seat of the falsehood. A
Sophistical Elenchus was skilful when it was difficult to see
whether the flaw was in the sequence or in the premisses : or
when there was no doubt as to this, but it was hard to say what
was the flaw in the sequence, or where the falsehood in the pre-
misses. When the Questioner had pointed his Elenchus, the
Answerer had to repel it if he could. His part shall be discussed
presently.
A Dialectical proposition is defined ^ to be a probable opinion,
prevalent among the many or among the philosophers, and
either universally held by the many or by the majority, or either
universally held by philosophers or by the most illustrious.
When the propositions that enter into Dialectical reasoning
are analyzed, they are found susceptible of the same division as
Scientific principles; some are limited,* others universal in
their application.* But while Science is chiefly characterized by
the former, its Theses, the common principles or Axioms being
scarcely perceptible, and only entering as canons of syllogism;
Dialectics, on the contrary, is not so much constituted by its
Organa,6 or specific principles, as by its common propositions or
Topics. Again, the Organa difier from the Theses of Science in
that they are not primary or original propositions, but merely
premisses of a specific character : for if they were properly prin-
ciples they would be undialectical.''
The Topics correspond to the Scientific Axioms, and proba-
bly many of them could be obtained from these by deduction.
Aristotle does "not give them in the form of propositions, but
• (rvKkoyia/ibe avriipamwg. — Soph. * iSia. ' Koivd.
Elench. 9. « Topics, i. 11.
= Soph. El. 33. 'S" 7^P ivrixV 'Apxaifi oiidn
' Topics, i. 1, and 10. AiaXeKriio) iarai. — Bhet. i. 2.
24 LOGIC OF OPINION.
only specifies the category or general conception that each in-
volves. Many of them could scarcely be reduced to proposi-
tions, but are merely hints or precepts to assist I'ls in conducting
the argumentation.
The Organa, or specific premisses, are of infinite variety, and
cannot, like the topics, be enumerated by the theory. They
should be arranged in the memory or common-place book in
their logical order.^^ They should be divided into genera, the
chief of which will be, Ethical, Physical, and Metaphysical.^
Definitions should occupy the first place, and then should come
the attributes: and the names of the philosophers who origi-
nated any paradoxes should be noted.
To illustrate the division of Dialectical propositions, we may
compare it with the analogous division that takes place in Rhe-
toric.
The Dialectical Theses correspond to the Rhetorical Issues. '
These latter are difierent in the three branches of Rhetoric, and
in each branch are various, falling under the categories of Fact,
Quality, and Quantity.
The division of Rhetorical premisses is similar to that in
Dialectics and Science.
Corresponding to the Axioms of Science and the Topics of
Dialectics are the Topics or Elements of Rhetoric. The name
of Maxim, which the Schoolmen gave them, may be explained
by Aristotle's definition of Element:* "Any thing of great useful-
ness and great simplicity."
The peculiar propositions of Rhetoric, that correspond to the
Scientific Theses and the Dialectical Organa, are its Specific ^
propositions, whether of wider ^ or narrower 7 application, and its
Singular 8 circumstances. These last occur in Rhetoric, which
treats of particular cases, but not in Dialectics, which, being of
a quasi-philosophical nature, is confined to universals.
' Topics, i. 12. also used in the Rhetoric : Trepi tVa-
' Plato, Sophistes, ^ 37. arovykvog tS>v Xoywy nXrifiiiivai do-
'■' a/iipiirliriToviiEva, — Rhet. iii. 5ai Kal irpoTaauQ. — Rhet. ii. 18.
* o civ 'iv bv Kai ftiKpdv £7ri TToWd ® Koivd.
y xp'h<"-l'-ov. — Metaph. v. 3. ' "iBia.
^ ASr). The word ykvoQ is used of ° t& i^ vrroyviov.
the Organa, Topics, i. 12, but it is
PIRASTIKE. 25
As the Organa or Generic propositions of Dialectics were di-
vided into three classes, Ethical, Physical, and Metaphysical; so
the Specific propositions of Rhetoric are ranged under three
chief heads. Honour, Justice, Expediency.
It may be observed, that Aristotle always uses the same or
similar terms to express the collection of Scientific, Dialectical,
and Rhetorical propositions. ^
After the enumeration of the Topics, directions are given to
the Questioner as to the order in which the questions shoidd be
arranged, and the manner in which they should be put.? As the
Answerer will be disinclined to make any concessions, the bear-
ing of which on the Thesis he perceives, it wiU be an object to
conceal the drift of each particular proposition. This may be
eflfected by mixing the essential propositions with others irrele-
vant, and by deranging the order of the essential propositions,
that is, proposing them unconnectedly and incoherently, not in
the sequence in which they will finally enter the syllogism. The
concealment is completely successful when the Answerer does
not suspect that he has lost his cause after the fatal concessions
have been made, till his opponent extricates and rearranges
them, and shows that they involve the contradictory of the
Thesis. The character of the opponent should be studied: some
from confidence in themselves and contempt of their adversary
will make any concessions at first, but afterwards grow more
Cautious : from such the necessary propositions should be drawn
before their fit of circumspection comes on. Others are excess-
ively cautious at first, but afterwards grow ashamed of making
so many difficulties, and become more liberal in their concessions.
The jealousy of these persons, says Aristotle, should be exer-
cised on indifferent matters, and the important propositions kept
back till they begin to suspect themselves of over-timidity.
Similar artifices are suggested, and some represented as fair,
others as Sophistical.' One of these is, to rouse the anger of
' licXIyeij/, kKXanPivuv. — AnaL irpoTaaeigiKKeKTEOv. — Topic8,i.l2.
Post. ii. 13. ^X"" i^eiKeyjiiva. — Bhet. ii. 23.
■TTporAaeig kKXafi^dvuv. — Anal. rpovog rfjg iKS.oyrjg TomKog (1. e.
Prior, i. 27. ttdiKog). — Ibid.
TrpoT&aug J/cMytii'.— Anal. Prior. = Topics, viii. 1.
i. 30. 'Soph. El, 12 and 15.
26 LOGIC OF OPINION.
your adversary by barefaced attempts at unfairness, as a dis-
putant is not so formidable when lie loses his temper! These
nefarious practices are pointed out of course for our avoidance:
besides, we have scarcely a right i to speak with reprobation of
Sophistry, unless we understand its character. Some artifices,
though unjustifiable against a fair adversary, are j ustifiable against
one who is unscrupulous himself: * but however fair, as far as he
is concerned, we must avoid them from respect for ourselves : '
and, if we follow Aristotle's advice, instead of meeting Sophistry
with Sophistry, we shall exercise a discrimination in choosing
our adversary, and avoid engaging with those who cannot ob-
serve the laws of honourable war&re.*
We now proceed to the duty of the Answerer : for though
the original province of Dialectics was merely the offensive pro-
cess, that of assailing a given Thesis,^ it soon proceeded to in-
vestigate the art of defence, and this province accordingly is
included in its definition. The theory of Solution is contained
in the short treatise on the Sophistical Elenchus, which ought
to be regarded as the last book of the Topics.
We may first, however, determine what propositions the An-
swerer may be expected to concede, and what he may claim to
withhold : ^ and the determination depends on the nature of the
Thesis he advocates; which must be either probable, improbable,
or indifferent, neither highly probable nor highly improbable.
If the Thesis is improbable, its contradictory, the conclusion of
the Elenchus, will be of itself probable; and as the premisses of
a syllogism ought always to be more probable than the conclu-
sion, the Answerer is not bound to grant propositions, however
probable, unless their probability is greater than that originally
possessed by the conclusion they have to establish. If the
Thesis is probable, the conclusion of the Elenchus wiU be the
reverse ; and then the Answerer ought to allow premisses which
' Soph. El. 16. ^ wairip yap ij Iv dyiSvi ASida
^ Soph. El. 17. eXdog n exei, koi sanv dStKOfiaxia
' SUaiov jiiv oiiK tvaxrinov ik. — ng- ovrag r/ tv dvTiKoyty, dSucoiia-
TopicB, viil. 13. X'« ioTtv kpiaTiKr/. — Soph. El. 11.
ov del avvtaravai evxipiSg irpbg ' Soph. El. 34.
Tovg TV%6vTag' avayxri yap jrovripo- * Topics, viii. 4.
Xoytav ffvfiPaiveiv, — Ibid.
SOLUTION. 27
though not highly probable, still possess a higher degree of pro-
bability than the conclusion. If the Thesis is neither probable
nor improbable, its contradictory is of the same character, and
propositions of but slight positive probability may be fairly
claimed. The same rule will hold, whether the probability or
improbability is absolute or relative to the creed of the particular
Answerer: and if the Thesis is not a tenet of his own, but of
some celebrated school or philosopher, reference must be had to
what was probable or improbable in that school, or in the views
of that philosopher : and if a third person succeeds to the cause
of one of the original disputants, he should govern himself by
the opinions of the person whom he superseded.
Before we proceed to Solution we will explain certain terms :
and we may observe, that there is great precision in the Dialec-
tical nomenclature.
Eristic and Sophistical reasoning are the same, but differ in
the motives from which they are employed. A fallacy is Eristic,
if prompted by the heat of dispute and the desire of victory:
Sophistical, ^ when employed from mercantile motives by a
pseudo-philosopher, who makes a trade of imaginary wisdom.
A Sophistry must be distinguished from a Pseudographema:
both are fallacies, ^ but the first is Dialectical, the second Scien-
tific. As a sound Dialectical argument differs from a sound
Scientific proof, becaiise the latter is confined to a particular
subject-matter, while the former is indiscriminately applicable
to several; so a Pseudographema is only practicable in a parti-
cular department, while a Sophistry is of a Protean character.
A Pseudographema* then, is defined to be a fallacy constructed
of the false principles peculiar to a particular science, and is
consequently intransferable.*
' aoipiaTiKol o\ So^ris x^P''" ^VS "£ ^ napaXoyttriioi.
XpriiiaTiaiiov' tj yap ao^uTTiierf ean ' ol ek ruiv irepi tivuq iiriaTrjiiaQ
XprilxaTiaTucri ng airb ao^iaq ipaivo- oiVeiwv yivofuvoi TrapoKoyuTfioi. To-
fikvrig. — Soph. El. 11. pics, 1. 1. kK riiSv dpx<^v Kal riiSv
Kal yap rj ao^uiTmri ian ipaivojii- ovinrcpatriidTwv riSv virb tijv tcx-
vri aofia ng dKX oiiK onjaa. — Ibid. vriv \(/evSoypa<l>€i. — Soph. Blench. II.
ean ycip ri aotpiarixri ipaivopivfi It does not appear that the name was
<ro^ia oiaa Sk nil' Kat 6 ao^iari^g ever applied to any but geometrical
XprjiianaTTtg dirb ^aivopivqg aotpiag, fallacies.
dSX ovK ovarig. — Soph. El. 1. ^ ouk Han fiertveyKHv Sid rb Ik
28
LOGIC OF OPINION.
A Sophistry or Dialectical fallacy is of three kinds : i it is
either
(1.) An argument whose premisses are false:
(2.) Whose premisses are inconclusive:
(3.) Or an argument which, though sound Dialectically, is
deceptive and Sophistical, because it professes to be Scientific,
1. e. to conform to the Appropriate method : or which professes
to be Pirastic, i. e. to show a deficiency of the Answerer in his
particular science.
As in Scientific proof it is not enough to show the fact, but
we must also show the reason of an attribute, so in Solution it
is not enough to prove that an argument is fallacious, but we
must also point out why it is a fallacy.^ Such a Solution is by
Enstasis, which is either Rejection ' or Distinction : * if a premiss
rwv iSioiv elvai dpx<Sv. — Ibid. The
following appears to be a case of
pseudographema. " Hobbes erro-
neously held that he had discovered
a means of geometrically doubling
the cube, a problem which cannot
be solved by plane geometry. He
proposed a construction for the pur-
pose : and when his critics had
proved that one of the lines in his
diagram would not meet the other
in the point which his reasoning
supposed, but in another point near
to it, he maintained in reply that
one of these points was large enough
to include the other, so that they
might be considered as the same
point." — Philosophy of the Induc-
tive Sciences, book i. 4, § 6. Com-
pare Aristotle's example : ry y&p
fl TO. riiiiKVKXia TTipiypdipeiv ji'fl i>e
Sii, rt ypafiiiaQ nvaQ ayuv jif) i>e ctv
dxOetTjffccVf rdv -jrapaXoyifffibv TroteT-
Tai. — Topics, i.l.
' ipsvSyg \6yog KoXuTai.
(') edv did if/evSuSv avjiiTtpaivii)Tai'
(') orav (paivrjTai (jviiinpaiveaBai
fufl avjiirtpaivoiiivog'
(') 'drav avjiirspaivriTai fiiv, fifi
fjivToi irpbg r6 TrpoKsifievov
C) 'oTav irpbg to TrpoKiifievov fiiv
avfiTripaivtirai, /irj jiivToi Kara tjjv
oiKelav jikBoSov. — ^Topics, viii. 10.
As the third is a case of Ignoratio
Elenchi, in the book on Fallacies
(chap. 11), it is included among the
second. The fallacy of non causa
pro causa would also fall under the
third of these heads. — Soph. El. 5.
^ As the preposition icnrd desig-
nates the cause of an attribute, so
the preposition irapa designates the
cause of a fallacy.
i^uTiv ri Avffig kfi^duiffig ^evSovg
ffvXKoyifffzod Trap OTToiav kptJTtjfftv
avfifiaivei rb \f/£vSog' Kal 77 tov <pai-
vofikvov avKkoyiajjiov irapd ri faivt-
Tai TiSv kpiOTTjfidTtitv. — Soph. El. 18.
i]v yap rf Avtrig kfifdviffig ^svdovg
avWoyia/iov trap' o ^j/svSrig. — Soph.
El. 24. " dvaiptng.
* Siaiptaig. That these were the
only legitimate kinds of solution
appears from several passages, e. g.
iroTipov irapd dvaipcaiv tj Siaipemv
iariv rj Xvmg. — Soph. EU 33.
SOLUTION. 29
is false, it must be pointed out and Rejected: if the premisses are
inconclusive, and there is only a semblance of syllogism, we must
point out the Distinction that separates it from a real syllogism,
and- specify the flaw it contains.
If the Answerer could not solve the Elenchus by Enstasis,
his last resort was to antisyllogize, that is, produce an indepen-
dent argument against the conclusion of the Elenchus.
This was however considered insufficient; because, though it
might show the falsity of the Elenchus, it did not show how or
where it was false : and besides, it broke through the division of
labour, by which the offensive was assigned to the Questioner,
and the defensive to the Answerer.
An inconclusive Elenchus must bear some resemblance > to a
genuine Elenchus, or else there could be no deception : its Solu-
tion therefore consisted in Distinction,^ or pointing out where
this resemblance failed. There were thirteen different heads of
these delusive resemblances, well known under the name of
Logical Fallacies, and to be found in the common books of
Logic, which we therefore need not explain.
The other kind of Enstasis is Denial, or Rejection. If the
reasoning is conclusive and the Answerer refuses to abandon his
Thesis, his only alternative is, to show reason why one of the
premisses should be Rejected: of course it would have been better
never to have made the concession, but if made, nothing is now
left but to retract it. His bare negation was insufficient : he had
to adduce an Homogeneous, Analogous, or Opposite case, or
might appeal to Authority.' Enstasis seems to have been re-
strained to these four topics, because it was desired, as far as
possible, to confine the reasoning to the Questioner, and to place
avu^aivei tiSv Xoyuv Toiig fiiv Phya. Anse. i. 3. See also the defi-
avWeKoyuT/uvovQ dvcXovra roig Sk nition of Ximg.
^aivojiivovg SuXovra \veiv. — Soph. ' yiverai Sid nvog o/toioTijTos. —
El. 18. Soph. El. 1.
bjrws r) dvaipovvreg r) Siaipovvreg ' Siaiptmg.
Xvaiiiev.—lbid. ' Anal. Prior, ii. 28. Rhet. il. 25.
tl yap dvaipei f) Siaipei 6 kvurra.- The same laxity was allowed to the
ixevog. — Topics, viii. 12. tpittriKSig Questioner in making a direct pro-
avXKoyiKovrai, xal yap ^ivSn Xafi.- position.— Topics, i. 8, and 12.
Pdvovai Kai davWoyiaroi ft'eri. —
30 LOGIC OF OPINION.
the Answerer in a purely defensive attitude. Why a preference
should he given to these particular four is not inconceivahle,
Authority was a topic peculiarly Dialectical, as appears from the
definition of a Dialectical proposition: Propositions relating to
Opposites are closely connected, and, mutatis mutandis, may be
considered identical: and Analogy or Induction is one of the
simplest modes of reasoning. An Homogeneous case is either
generic, or specific to the subject of discussion.
Yet there was no reason why the other topics should be abso-
lutely excluded : they were admitted, then ; but this mode of
objecting to a premiss was not considered Enstasis, but Anti-
syllogism.i This latter term then is not only applied to a syllo-
gism framed by the Answerer against the conclusion of the
Elenchus, but also to a syllogism directed against a premiss,
when it falls under any topic other than the four that constitute
the Enstasis.
What is said of Enstasis in the Prior Analytics only applies
to Enstasis by Rejection, and only to one of the four forms of
this.
In the Rhetoric we have a similar account of Solution,^ which
is divided into Enstasis and Antisyllogism : ' and we have some
further observations on the mode in which the Sign, Tekmerion,
Induction, and Verisimilitude are enstatized.
Signs can be always enstatized by Distinction, as they are
always inconclusive : the Tekmerion can only be enstatized by
Rejection, as its sequence is unexceptionable. It is not a sufiicient
Rejection of Inductive propositions and Verisimilitudes, to ad-
duce singular exceptions; this only shows they are not universal:
but we must also show that they are not general ; for generality
is enough for the opponent.
The account that has been given of Pirastike will apply with
but slight modification to Dialectics in general : the former
employs any premisses that the Answerer chooses to grant,* be-
' This appears from the following li. 25.
El oiv iiijTE dvTemx^ipsXv ' v 'ivaraaiQ rb i'nruv do^av nvd
E%wi/ firiTe kvi(TTaa6ai oi riOjjfftf Sij- e? r/g 'itrrat SijXov '6ti ov cwWeXoyt-
\ov oTi SvdKoXaivtt. — Topics, viii. 7. arai fj '6n TpsvSog ri t'iKti<ps. — Ibid.
^ tan Sk Xveiv ^ dvTiavWoyiad- ^ ol kx tSiv tov diroKpivofikvov do-
fiEVOv t) evffTatTiv iveyKOVTa. — Rhet. ^Gtv. — Soph. El. 2.
LOGIC OF INDUCTION. 31
cause its object is to discover his views and to test their sound-
ness : whereas Dialectics only employs propositions of an
absolute probability ,i opinions that are current in the public at
large.
As the object of the Questioner is to obtain premisses or
nniversals, which, when they are not obvious, must be claimed
inductively; and as the object of the Answerer is to withhold
them, which cannot be done, if they are at all probable, without
specifying his objection, or showing cause why the Induction
should not be admitted; Dialectical power, which embraces both
of these functions, will consist of two elements \^ talent of Pro-
position, and talent of Enstasis; that is, the power of descrying
Identity, or Unity in Plurality, and the power of descrying
Diversity, or Plurality in Unity.^ These are the two original
gifts of the scientific faculty,* called, in the language of Kant, the
powers of Generalization and Specification ; and not only do they
constitute the antagonistic powers in all controversy, the one
attempting to construct what the other attempts to destroy, but
their harmonious action is required in all positive philosophy, the
one providing unity and system, the other multiplicity and arti-
culation.
§ 6. D. We may now proceed to Dialectics as an organ of
the Inductive sciences. We have already seen that this is one
of the uses of which Aristotle considered it capable.* In another
place ^ its power of examining hypotheses is pointed out as
making it a useful organ for philosophy, and the habit of En-
stasis is mentioned as a safeguard to the accuracy of the philoso-
pher's Induction : the Enstasis '' in this case being limited to
' oi EK tStv ivSo^iDv (rvKKoyuxTiKol ' Jrpig ret irpioTa twv wepl tica-
dvrt^dffetog. — Soph. El. 2. ffTTjv STnffTrtfttjv cipx&v xp^fft/toff ri
' SiaXtKTUcbg o iTpoTaTiKog xai iv- SiaXeKTiieri . . . c^iTatrriKti ydp ovaa
araTiKOQ. — ^Topics, viii. 12. irpbg r&g airaaiav rSv /itOoSiov &p-
' tan Sh rb /ikv TrporiiveaOai %v x^S bSbv Ix"- — Topics, i. 2.
rrouiv rd irXetfti, rA Si kviaraaOai rb ^ irpbg rffv Kurd ^iKoao^iav ^p6-
tv iroXXa. — Ibid. vr/mv rb SvvaaBai avvopdv xai avv-
' TOVTiav iyitiye ipaarrlg tUv Suu- ewpaKsvai rd d0' iKoripag av/ilSai-
psatutv Kai awayiay&v (cat Tovg Sv- vovra rijg iiTrodkating oii fiixpbv op-
vafiEvovg tig ^v Kal ewi TroXXa tts^u- yavov' Xombv ydp tovtow bp9&g
Kbg bpdv KoKiS SidKfKTiKovg. — Plato, eXiaOai Qdrtpov. — ^Topics, viii. 12.
Phaedi'us, ^ cxi, ' StX IvtrrariKov ilvai Sid tUv oi-
3-2 LOGIC OF INDUCTION,
phaenomena obtained by exact observation of tlie subject in-
vestigated.
The method of investigating first truths employed by Ari-
stotle i is to state the principal phaenomena to be accounted for,
and then examine the hypotheses that had been proposed for
their explanation, and, if none appeared tenable, to advance a
theory of his own. This examination would necessarily assume
a Dialectical form ; the method of criticising all hypotheses
would find its highest employment in criticising those offered
for our acceptance as supreme scientific laws. These, according
to the Aristotelian analysis, would assume the form of defini-
tions ; and accordingly, in the following treatise, when we have
arrived at the discussion of Definitions, we shall be referred to
Dialectics as the final criterion of their correctness. ^
The point we now stand on is the weak point in the Aristote-
lian Logic, the weakness that rendered the Baconian revolution
necessary before the Physical sciences could be founded on a
solid basis. It is true that the Inductive method cannot resem-
ble the Deductive, but it does not therefore follow that it is
identical with the method of Opinion. This is recognized by
Aristotle himself in the passages quoted above, where the
latter is contrasted with the Physical or Inductive procedure.
If Opinionative Logic includes all modes of reasoning not purely
DemoJistrative, then Inductive Logic ought to consist of a
selection from these, rigorously excluding all that admit a
possibility of error. But no such separate theory or selection
seems to have been made by Aristotle, and in his actual inves-
tigation of scientific principles we find no rigid abstinence from
the more precarious lines of argument.
Besides the laxity of his Topics, he was infelicitous in the
objects which he proposed to accomplish by these methods.
His account of a commensurate proposition, where the presence
or absence of the subject involves the presence or absence of the
predicate, cannot but remind us of what Mr. Mill has called the
laliav kv<rrd(re<i>v iv Tip ykvcf tovto tion of Conceptions and Colligation
S' lariv iK Tov Trdaag TeBiuiptiiekvai of Facts, book ii. j De Coelo, i. 10 ;
Tag Siafopdg. — Do Ceelo, ii. 13. Met. i. 3 ; Met. iii. 1 ; De Anima,
' See the Philosophy of the In- i. 1 and 2.
ductive Sciences : on the Explica- ' Post. Anal. ii. 18.
DEFECTS OF THE SYSTEM. 33
Methods of Agreement and DiiFerence ; and if, instead of Topics
to establish the various kinds of Predicable, Aristotle had set
himself to ascertain rigorous methods for the determination of
such propositions, he might have approximated much nearer
to the perfection of the modern Logic. Although the ultimate
laws may appear in the form of Definitions, it is a great mis-
take, as Bacon often observes, to proceed too precipitately to the
discovery of these, instead of gradually advancing to them
through laws of increasing generality from the primary laws,
the immediate generalizations of phsenomena. Rules for the
ascertainment of causal connections would have been more
valuable than methods for the establishment of the Predicables :
but though a scientific definition should express the cause of the
object defined, no notice is taken of this in the Dialectical
Topics for the establishment of Definition. A proposition
expressing a Property is commensurate, but if we examine the
Topics for Property, we shall find that they rather relate to the
incidents of verbal controversy, than to the establishment of
scientific laws.
Plenty of writers have declaimed in vague terms against the
old method of investigating principles, but none has indicated
the exact points in which it difiered from the new. And yet
our knowledge of the latter would be more complete, if we knew
its relation to the one it superseded ; and now that the true
method is so firmly established, there is no reason for exagger-
ating the defects of the old, or danger in acknowledging the
degree, whatever it was, in which it approximated to the truth.
Besides the circumstance already mentioned, the laxity of the
Topics, or methods of arguing from phsenomena, and the infeli-
citous choice of the ends proposed to these Topics, another vice
in the old system was the paucity of these original phaenomena,
and the carelessness with which they were collected.
We have a general recognition of the fact that the Physical i
sciences must rest on induction, both in the passages already |
cited, and in others that might be adduced ;i for Aristotle \
• clpiiKaai fiiv, ov KoKuie Si, dW r&e irepi iKaarov Ifiinipiag tan Tta-
cLWUporkpiDQ tSv avu^aivovTiov. — paSovvai .... XriipOkvTiav yip Ua-
De Respir. 1. iib ris fiiv apxaq vS>q tSiv ipaivo/iivuiv ovtoiq evpiOi]-
F
34 LOGIC OF INDUCTION.
stands in about the same relation to his predecessors in which
Bacon stands to himself, and the expressions he uses in criti-
cising their method often reminds us of the language of Bacon.'
Indeed the apparent similarity of Bacon's method to that
which it proposed to supplant, was one of the greatest obstacles
to its introduction. For it appeared to have already had its
trial, and if theoretically it might corrtain some minute points of
difference, it was expected that these would vanish in the un-
avoidable shortcomings of practice. StiU the prejudice against
Sense created by the enthusiastic declamations of the ancient
Rationalists was perhaps not completely eradicated, and the
mathematical precision with which phsenomena are now mea-
sured, and the method with which they are registered, did not
enter into the Aristotelian conception of Induction : and we
have an example how near the mind may approach to the recog-
nition of a principle, and yet remain in darkness ; and how
enormous a difference results from the complete possession of a
great idea, and the half-true state of mind, that has partly given
in its adherence to the truth, and partly remains in compromise
with error.
'j But a still greater defect than the faultiness of its Observation
I was the complete absence from the system of the idea of Ex-
J periment. Observation takes cognizance of the phsenomena
which nature presents of her own accord; whereas Experiment
creates others for itself, and has the advantage, where it is ap-
plicable, of selecting the conditions under which it wiU view the
subject-matter, under which perhaps it is never presented by
nature; and of knovnng precisely what these conditions are, as
they proceed from our own arrangement : whereas in Observation
we are often uncertain whether we have noticed all the antece-
dents and concomitants of a given phaenomenon. Hence it is
that Aristotle's success is very different in the sciences that rest
on Observation and those that rest on Experiment. In the Poli-
aav ai auTpoXoyiKal oiTroSii^tiQ .... Xdywv iStwpijroi rwv inrapxovTuiv
£1 yap firiSlv Kara, riyv iaropiav va- &vTtg irpbg bXiya STn^Xs^avrce Awo-
paXeiipBeiri twv aKj]6u)s {nrapxovrojv tpaivovrai p^oK, De Gen. et Cor. i.
rote irpdyfiaai, &c. — Prior. Anal. 2, with Bacon's : Istud respicere pau-
i. 30. ca et pronunciare secundum pauca
' Compare : ol S' ek tSiv ttoWHv perdidit omnia.
DEFECTS OF THE SYSTEM. 35
tical sciences which rest on Ohservation, or rather on Experience,
that is, where under any tolerable state of society Nature herself
is sure to supply the sensations requisite for eliciting the ulti-
mate laws and dominant ideas, it would be difficult to find any
writer in later times by whom he has been surpassed or equalled :
and his Zoological treatises, where Observation rather than Ex-
periment was required, are spoken of with high praise by modern
naturalists. In Chemistry, on the other hand, of which the
beginning, middle, and end is Experiment, he was completely
unsuccessful ; and an error in so elementary a science could not
fail to bp widely felt in the other branches of his Philosophy.
He complains of the difficulty of discovering primary laws,
and seems to confess the unfinished state of Inductive Logic. ^
So much for his Inductive Method.
The treatises contained in the Organon, though incomplete,
perhaps take us over most of the ground that should be explored
by Logic. One important deficiency is the method of the Meta-
physical sciences : for the evolution of Metaphysical ideas cannot
be inductive, as their objects do not belong to the sensible world.
Aristotle may have acquiesced in the views of Plato, who seems
to hold that the highest ideas of Reason are developed by lower
but analogous perceptions.''
Some Logical doctrines might be gathered from the other
works of Aristotle, such as that which Kant calls the Maxim
of Parsimony.^ The Organon is by no means all that Aristotle
wrote on the subject of Logic. In the list of his works given by
Diogenes Laertius we find about twenty other Logical treatises :
among them the Methodica, quoted in the Rhetoric, and consist-
ing, according to Laertius, of eight books; which probably con-
' TrdvTti Sk Kul TravTbiQ sari tSiv jShv Trepi SKaarov rig o rpoiroQ. — De
XaKi'torraToyv Xa^tlv nvh vianv Anim^, i. 1 .
wipi TJjg ^xve' I'"-'- y^P ™X' ^'' '''V ' iiravAvai. &aircp ivava^aQiiols
S6%eu fiia ng dvai iisBoSog xard. xP<*/*''"»'- — ^1**- Symposium.
iravTiav Trepl Hv PovXa/ieOa yvCtvai ' ^avipbv '6n jiaKpif PsXrtov we
T^v ovaiav, iivirep «ai t&v sark iXaxiarag troulv T&g ipx^Q, vav-
(rv/ijSe/SijKoe iSiuv AiroSuKiV d Sk fii) ruv ye t&v avrav ntWovTiirv Stl-
iari Ilia koX Koivi] Tig piOoSog irtpi Kvvadai, Kadamp d^wvn xai ol iv
TO ri iariv, in xaXfTTiliTtpov yiverai ToXg fiaBrinamv. — De Coelo, ili. 4.
TO irpaynaTiieirBai' Stijvn y&p \a-
36 LOGIC OF INDUCTION.
tained a more systematic view of the whole of Logic than any of
those that survive.
We now conclude our sketch of the Organon, which we have
divided into four parts; General Logic, the Logic of Deduction,
the Logic of Induction, and the Logic of Opinion: the third
indeed not sufficiently articulated and disengaged from the
fourth, and hence the necessity of a Novum Organum.
THE
POSTERIOR ANALYTICS
BOOK I.
CHAPTER I.
ON REASONING.
§ 1 . All teaching and learning by way of inference proceed
from pre-existent knowledge. Of this we may be satisfied by
examination of instances : it is thus that the Mathematical
sciences and the Arts are acquired ; the Dialectician's Induction
and Syllogism both appeal to previous knowledge, the one of
the phaenomenon, the other of the law : and the Orator per-
suades by Example and Enthymeme, the one a kind of Induc-
tion, the other of Syllogism.
§ 2. The previous knowledge is twofold : it is a Judgment,
and afiirms the existence of an object : or it is a Conception, and
comprehends its nature : or it is a union of both. That one or
the other of two contradictories is necessarily true, must be
affirmed in a Judgment:' the nature of the triangle must be
comprehended in a Conception : and we must both comprehend
the nature of the Unit and affirm its existence : and these ele-
ments of knowledge have not always the same evidence.
§ 3. When, however, implicit knowledge is rendered ex-
plicit, the universal premiss may be antecedent to the conclu-
sion, while the singular is simultaneous.* If, for instance, the
equality of the interior angles of every triangle to two right
angles is antecedently known, ^ as soon as the existence of a
particular triangle in the semicircle is given by observation, (for
' We have here the three kinds of plicit knowledge. See Prior. Anal,
scientific principle, which we shall ii. 23. and Nic. Eth. vii. 3.
presently find are Axioms, Defini- ^ rjij,g g^mg gxample of immediate
tiona, and Hypotheses. perception is adduced, Nic. Ethic.
» yvapiZuv, actual knowledge, is vi. 8.
opposed to EX"" T^v yvSaiv, iva-
40 ON REASONING.
singTilar premisses are objects not of inference, but of observa-
tion,) our knowledge of the conclusion is simultaneous.
§ 4. Before the minor is observed and the syllogism con-
structed, the conclusion is in one point of view known, in
another unknown. Before we know the existence of a subject,
we cannot without qualification be said to know what attribute
it possesses : we may be said to know it implicitly, or in the
universal ; but only with such a limitation. This is the way
we must solve the dilemma in the Meno, by which it is argued
that we can learn nothing, or else only what we already know, i
The other solution (which denies that we know the universal
when ignorant of the particular) is inadmissible. If you pro-
fess to know a universal, for instance, that all Twos are even,
they refute you by producing a Two whose existence was un-
known to you, and whose evenness consequently, they argue,
you cannot have known ; maintaining, that you knew, not that
all Twos were even, but that every Two, whose existence was
known to you, was even. This is inadmissible ; for your know-
ledge was derived from demonstration; and demonstration
makes no reserve of the kind, but pronounces upon all triangles
and numbers without exception. The true solution then is,
that you knew in one sense what you were ignorant of in ano-
ther. It is not inconceivable that we should learn what we
u already know in a different point of view : but it would be,
" that we should know and not know one and the same thing in
one and the same point of view.
' See Meno, § 14. It was argued Axiom which asserts that no sub-
that inquiry is useless, and that ject is capable of contradictory pre-
nothing can be learnt: for what is dicates.
known is not an object of inquiry ; In modem times, the fact that we
and what is unknown it is useless to have an implicit knowledge of the
search for, as it could not be recog- conclusion when we know the pre-
nized even if found : and to say that mioses, has brought on the syllogism
the same thing might be both known the charge of petitio principii.
and unknown, seemed to violate the
[41]
CHAPTER II.
SCIENTIFIC PRINCIPLES.
§ 1. Absolute science, as distinct from the Sophist's^ acci-
dental science, is, according to the common conception, Know-
ledge of the necessity and the reason of a law. Science must
be this : for both the real and the fancied possessors of absolute
science ascribe to it the investigation of necessary laws. We
may afterwards see if there is any other kind. It is certain there
is such a thing as demonstrative knowledge: demonstration
means scientific proof: and the possession of scientific proof is
science.
I Assume this definition, and the premisses of demonstrative
science must be true, elementary, immediate, clearer than the
conclusion, antecedent, and causal; and then the principles will
be appropriate to the conclusion. Proof may exist without these
conditions, but not science nor demonstration.
§ 2. The premisses must be true. Science cannot be false :
we cannot know that the diameter is commensurate.
§ 3. They must be elementary, and indemonstrable; else
they wiU need demonstration: for the demonstrable is only es-
sentially known by demonstration.
§ 4. They must be causal of the conclusion, clearer, and
antecedent: causal, because to know the cause is the very es-
sence of science : antecedent, both as causal and as foreknown :
foreknown, not only as conceptions, but also as propositions.^
Priority and pre-evidence are of two kinds. What isnaturally
prior and clearer is not prior and clearer to man : the objects
which are farther from sense are absolutely prior and clearer:
those which are nearer to sense are prior and clearer to man.
' The predicate of a scientific pro- scientific, is Sophistical,
position is Essential : the predicate " That is, the principles of Science
of a dialectical proposition is Acci- must include Hypotheses, or Postu-
ilental : a proof founded on dialecti- lates, as well as Definitions,
cal propositions and professing to be
42 SCIENTIFIC PRINCIPLES.
The latter are particulars, the former universals, so that they
are opposites to one another.
§ 5. They will be elementary because they are the appro-
priate principles : for Element and Principle are synonymous. A
demonstrative principle is an immediate or proximate proposi-
tion. A proposition is either of two enunciations, and has a
single subject and predicate : if dialectical, it offers an alternative:
if demonstrative, it determines which is true. Enunciation is
either of two contradictories. Contradiction is opposition which
excludes an intermediate: the side which conjoins subject and
predicate is affirmative ; that which disjoins them is negative.
§ 6. Immediate syllogistic principles are either Theses;' that
is, are indemonstrable, but not the necessary antecedents of all
inference : or Axioms ; that is, are indispensable for any progress
in knowledge. Such principles as the latter there are, and this
is the name we generally give to them.
A Thesis may be one side of an enunciation, and assert the
existence or non-existence of a subject; and is then called an
Hypothesis : or it makes no assertion, and is called a Definition.
The arithmetician, when he defines the Unit as an indivisible
quantity, makes a Thesis, but not an Hypothesis : for to unfold
the essence of a subject is not the same as to affirm its existence.
§ 7. Belief and knowledge of the law being grounded on de-
monstration, and this standing in the strength of elementary
laws, some or all of the elementary laws must be not only fore-
known, but with a higher knowledge than the conclusion :, the
cause which imparts a predicate to a subject always possessing
that predicate in a more eminent degree: as the primary object
of affection is dearer than another object which is loved for its
sake. The primal laws, the origin of our knowledge and belief,
must be the object of higher knowledge and belief than the deri-
vative laws of which they are the vouchers. Now a truth cannot
be believed more than other truths whicR are known, unless
itself the object of knowledge: the grounds of demonstration are
therefore the objects of knowledge, as some or all of them must
' The Theses correspond to the or Topics of Rhetoric and Dialectics,
specific principles of Rhetoric, and For an account of the Axioms and
to the Organa of Dialectics: the Hypotlieses, see Appendix A and B ,
Axioms correspond to the Maxims
FIRST TRUTHS. 43
be grasped with a firmer faith than the demonstrated law. And
knowledge and faith in the primary truths must not only be
greater than that in the conclusion, but also than that in any of
the opposite principles, from whence the antagonistic errors might
be educed. For perfect science must be impregnable.
CHAPTER III.
THE FIRST TRUTHS* ARE KNOWABLE, BUT NOT
DEMONSTRABLE.
§ 1. From the necessity of knowing the primary laws, some
have maintained that science is impossible ; others, that science
is possible and all laws demonstrable : neither of which doctrines
is necessary or true.
The impossibility of science is maintained by a dilemma:
Either there is no limit to the regression, no primary law; and
then, as we cannot traverse an illimitable series of antecedent
laws, there can be no science : or, if there is a limit to the re-
gression, as demonstration is the only source of science, the
primary indemonstrable laws must be unknown, and the conclu-
sion merely hypothetical, not categorical and scientific.
The others, though they hold, with these, that demonstration
is the only source of science, contend that all laws are demon-
strable by a reciprocal and circulating evidence.
We maintain that demonstration is not the sole source of
science ; that the science of immediate truths is not demonstra-
tive. If we demonstrate by prior and more elementary laws,
the immediate laws, where regression ceases, must be indemon-
strable.^ Further, we assert that, besides science, man possesses
a faculty that begins science, the faculty of Ideas.
§ 2. Absolute demonstration cannot be circular, for these
reasons. Firstly, the ground of demonstration is prior and
more evident than the conclusion ; and one and the same law
cannot be both prior and more evident, and posterior and less
evident. It may possess the one character absolutely, and the
' This question is resumed chap, xix — xxii.
44 UNIVERSAL, ESSENTIAL, COMMENSURATE.
other relatively to man : and it is its relative character which
determines its position in Induction. But our definition of
ahsolute science need not be enlarged ; for that which is
merely prior to man cannot be the ground of absolute demon-
stration. ^ Secondly, circular demonstration only proves that a
theorem is true, if it is true : in which manner any theorem may
be established. Assume three terms (for it is immaterial
how many or few terms compose the circle). In regular proof,
when theorem A establishes theorem B, and this again theorem
C, we have theorem A in warrant for theorem C. In circular
proof, A recurs instead of C ; so that theorem A is warrant for
theorem A. Any theorem may be thus warranted. Thirdly,
even this proof is impossible except for reciprocals, such as pro-
perties. One term or premiss gives no conclusion : two pre-
misses make an elementary syllogism. We showed, when
speaking of syllogism, that if the terms A, B, C, reciprocate, all
their possible conjunctions are capable of circular proof in the
first figure : and we also showed that it could not be constructed
in the other figures. Only propositions that are simply con-
vertible are capable of circular proof; and as these are rare, it
is an idle and untenable assertion that demonstration is circular,
and all truths demonstrable. '^
CHAPTER IV.
UNIVERSAL, ESSENTIAL, COMMENSURATE.
§ 1. The conclusions of absolute science are necessary: the
premisses of demonstration therefore are necessary. In order
to examine their character, let us define Universal, Essential and
Commensurate.
§ 2. An attribute is universal that is possessed by a class,
without exception of individuals or of times. Animal is a uni-
versal predicate of Man i^ and wheresoever and whensoever we
can predicate Man, we can also predicate Animal. Point is a
■■ Knowledge is not Science till it ' See, however, book ii. 11.
has reached the deductive state.
UNIVERSAL, ESSENTIAL, COMMENSURATE. 45
universal attribute of Line. For we assail a universal proposition
by adducing an individual of which, or a time when, the predi-
cate is not true.
§ 3. An attribute is essential that enters into the concep-
tion ofthe subject;! as Line enters into the conception of Triangle,
and Point into the conception of Line. It helps to compose the
essence of the subject, and it is found in its definition.
Or, it is an attribute in whose definition the subject is con-
tained.2 Straight and Curved are attributes of Line; and even
and odd, prime and compound, square and scalene, of number:
and we cannot define them without mentioning the subjects they
attach to, line and number. Those predicates which satisfy
neither of these conditions are accidental : as White and Musical
with reference to Aninial.
In another sense, that is essential which is not ascribed
to any subject as an attribute : as Substance, which requires
nothing else as substratum of its existence. What is thus
ascribed is accidental. White and Walking are ascribed to a
subject that is white and walks. In another sense, a concomi-
tant that is caused by an antecedent is essential. Death is an
essential concomitant of Beheading. But it is accidental that
it lightens while you walk.
In the essential propositions of absolute science, the sub-
ject is either contained in the definition of the predicate, or
contains the predicate in its own definition; the essence of the
terms is the cause of their conjunction : and their conjunction is
necessary. The subject necessarily possesses a determinate pre-
dicate, or at least the alternative of two contraries. Line must
be either Straight or Curved ; Number must be either Odd or
Even. Contrariety is the privation or contradiction of a, quality,
in a subject of the same kind as another which possesses the
quality. That which is not odd, and belongs to number,
the class, to which oddness attaches, is even. Therefore, as
' From the force of the preposi- x" """■' ovaiav xai xard to (ldo£,
tion, Kaff avrb includes the notion ch. xxxiii. if ycip Kaff avrovirapxu
of Causation. A predicate is essen- « tovto avrb avTif oLnov, ch. xxiv.
tial when the subject itself {airh), "^ Met. vii. 5 ; Phys. Ausc. i. 3 ;
or its essence, is the cause of its con- ov vira^xii iv rif Ady^i tovto if
nection with the predicate : vTrap- avfi^kfiriKe. Also Post. Anal. i. 22.
46 COMMENSURATE.
one or the other of two contradictories must be true, one or the
other of such essential predicates must be true.^
§ 4. A ^commensurate attribute is universal and essential, and
belongs to the subject as it is what it is, and is therefore neces-
sary. The term, Essential, is equivalent to the term. As it is
what it is. A line Essentially, and As it is what it is, contains
a point, and is straight. A triangle Essentially, and As it is
what it is, contains angles equal to two right angles.
An attribute is commensurate to the primary or highest
genus of which it is universally predicated. The attribute of
containing angles equal in sum to two right angles is predicable
of Figure, but not universally. It is predicable of Isosceles tri-
angle, universally but not primarily. It is universally, and pri-
marily predicated of Triangle. Where it is both universally and
primarily predicable, it is commensurate. Of Triangle it is de-
monstrated primarily, commensurately, and essentially. To
Isosceles triangle it is not commensurate nor essential.
CHAPTER V.
COMMENSURATE.
§ 1. It often happens that a conclusion is not primary and
commensurate, when it seems to be. When there is no genus
of the individual or individuals ; or when there is a genus, but a
nameless one, and the individuals differ in species ; or when the
predicate has been proved of a species ; we are liable to this
mistake. The conclusion, though not primary and commensu-
rate, is universal. If not primary and commensurate, the de-
monstration is not essential. Perpendiculars to the same line
are parallel ; but this is not an essential proposition ; for not
' This principle is the Axiom. used as synonyms : and even in the
' Ka9d\ov is generally translated present his practice is not uniform,
Universal, but it was necessary to so that sometimes it is uncertain
use another word, in order to distin- how Ka66\ov should be translated,
guish it from xard ■jravrog. In In book ii. 14 the definition is ex-
Aristotle's other works they are pressly abandoned.
COMMENSURATE. 47
only perpendiculars, but all lines that meet another at equal ■
angles, are parallel. Were the isosceles the only triangle, the
property of containing angles equal to two right angles would
seem essentially connected with isoscelism. The permutation
of proportionals, numbers, lines, solids, times, is not essentially
connected with number, time, dimension, but can be demon-
strated at once of the commensurate genus. It was formerly
proved in detail. They differ in species, and there was no
name for their genus. When you prove in detail of each
species of triangle, equilateral, scalene, isosceles, the equality of
their interior angles to two right angles, you may exhaust the
possible cases, but your predicate is not essential and com-
mensurate, and you have only a sophistical science. Your Uni-
versal, though numerical, is not Essential.^
§ 2. What is the criterion of a scientific and commensurate
conclusion ? If Triangle is essential to the predicate, and the
essence of Isosceles is the same as the essence of Triangle, the
conjunction of Isosceles and the predicate is Scientific. What
subject is essential, primary, and commensurate ? The primary
or lowest genus, that cannot be eliminated without the destruc-
tion of the predicate.^ The interior angles of a brazen isosceles
triangle are equal to two right angles. Brazenness and Isoscel-
ism maybe eliminated, but not Figure. But lower genera than
Figure are also ineliminable. If Triangle is the primary or lowest
ineliminable genus, it is essential and commensurate.
' Essential propositions are found- tlieir difference of view on this sub-
ed on definitions (see chap, iv), and ject affects their Metaphysics, not
the object of definition is the clSog. their Logic.
See also chap, xxxiii, {/■jrokriipeTai ' Commensurate propositions
ijrapx"*" K'"'' ovaiav Kai xarct to should be the objects proposed for
tlSoQ. The knowledge, then, of the discovery by the methods of Induc-
«Z5oe is necessary for science, accord- tion. See Mr. Mill's System of
ing to Aristotle as well as Plato ; Logic, book ii.
[48]
CHAPTER VI.
SCIENTIFIC PRINCIPLES NECESSARY, THEREFORE
ESSENTIAL.
§ 1. Scientific conclusions are necessary, and are therefore
educed from similar premisses. This condition is not satisfied
by accidental attributes, but is by essential : for here the predi-
cate enters into the definition of the subject ; or the subject
enters into the definition of the predicate, and must exhibit
one of two contraries. The premisses of demonstration are
therefore essential.
§ 2. Or we might have proved the necessity of demonstrative
premisses by assuming the necessity of the demonstrative con-
clusion. And if the premisses are necessary, not merely true,
the proof is demonstrative. We imply the necessity of demon-
strative premisses, when we assail a supposed demonstration by
urging that there is no necessity in the conclusion, or none
evinced by the proof. It is therefore a great mistake to suppose
that our principles are rightly selected, if only probable and
true : as the Sophists assume, that to know is the possession
of knowledge.! A principle requires more than probability and
truth ; some truths are inappropriate. A principle is the ele-
mentary law appropriate to a particular subject-matter.
Another consideration will prove the necessity of the pre-
misses. You have no science of the demonstrable till you can
explain its reason. If the major term is a necessary predicate
of the minor, and the middle term of your demonstration is not
necessary, you cannot explain the reason. If your middle term
is not necessary, it cannot explain the necessity of the conclusion.
Again, if "at present you have no knowledge of a truth,
which remains unaltered, while you remember your former rea-
son ; you had no knowledge before.^ If your middle term is not
necessary, it may cease to be predicable : then, remembering
your former reason, you will not know the truth, which remains
unaltered. If the middle has not actually ceased, but may
' See Plato, Euthydemus, § 16.
' This argument is taken fi-om the Theaetetus, 4 55.
'IT'
SCIENTIFIC PRINCIPLES NECESSARY. 49
sibly cease, such a situation is possible, and such possibility is
inconsistent with science.
A conclusion may be necessary, though the middle by which
we prove it is contingent ; just as it may be true, though the
premisses by which we establish it are false. But if the middle
is necessary, the conclusion must be necessary ; as it must be
true, if the premisses are true. A is a necessary predicate of
C, if A is necessary to B, and B to C. If the conclusion is con-
tingent, the middle cannot be necessary. Let A be a contingent
predicate of C. If A were necessary to B, and B to C, A would
be necessary to C : which is contrary to hypothesis.. In de-
monstrative science the conclusion is a necessary law ; and if
your middle term is not necessary, you will not know the rea-
son of the necessity, nor even the necessity, of the law. Should
you indeed mistake contingent premisses for necessary, you will
believe without knowledge the necessity of the conclusion :
without this mistake, you cannot even believe in the necessity
of the law, neither knowing the fact from mediate, nor the rea-
son from immediate premisses.
§ 3. Unessential attributes are not objects of demonstrative
science : they cannot be necessarily concluded. It may be
asked of what use they are as premisses in Dialectics, if they do
not necessitate the conclusion. Do we not first make some
irrelevant remarks, and then assert the conclusion, when we
argue from contingent premisses ? To which we answer, that
they are not propounded as grounds of a categorically necessary
conclusion ; but because, if they are conceded, by a hypothetical
necessity the conclusion is conceded ; and if they are true, by a
hypothetical necessity the conclusion is true.
§ 4. Essential attributes, then, are necessary to their peculiar
subject-matter, and form the conclusion and premisses of scien-
tific demonstration. Accidents, not being necessary, and even if
universal, not essential, do not teach the reason of a law. This
happens in proof by signs. The conjunction may be essential,
but you do not know it as such, nor do you know its reason.
You know the reason when you know the cause ; and when the
j^l^^inction of the terms of your syllogism, major and middle,
iB^^ and minor, is caused by their own essence.
[50]
CHAPTER VII.
SCIENTIFIC PRINCIPLES ARE APPROPRIATE AND
INTRANSFERABLE.
§ 1. One science cannot employ proofs borrowed from
another. 1 Geometrical truth cannot be proved by Arithmetic.
For demonstration is analyzable into three elements ;2 the
demonstrated major, an attribute essential to a particular mat-
ter ; the axioms, or syllogistic canons ; and the subject-genus,
whose properties and essential attributes are proved. Of these
the axioms, or syllogizing powers, are common to all sciences.
But if the subject-genus of Geometry is different from the sub-
ject genus of Arithmetic, Geometrical attributes cannot be
proved by Arithmetical demonstration. Such transference
' " But, in order that we may
make any real advance in the
discovery of truth, our ideas must
not only be clear; they must also
be appropriate. Each science has
for its basis a different class of
ideas ; and the steps which consti-
tute the progress of one science can
never be made by employing the
ideas of another kind of science.
No genuine advance could ever be
obtained in Mechanics by applying
to the subject the ideas of space and
time merely; no advance in Che-
mistry by the use of mere Mechani-
cal conceptions ; no discovery in
Physiology by referring facts to
mere Chemical and Mechanical
principles. Mechanics must involve
the conception of Force ; Chemistry
the conception of Mlementary Com-
position ; Physiology the concep-
tion of Vital Powers. Each science
must advance by means of its appro-
priate conceptions. Each has its own
field, which extends as far as its
principles can be applied." — Philo-
sophy of the Inductive Sciences,
book ii. 2.
^ £t Sk OiTroSuKTLKTJ 'jr€pi ai/Tixiv
lari, Seiim ri yevog tlvai viroKetne-
vov, Kal T& fikv TraOri rd Sk A^iMiiaTa
airiSv avayKti y&p £k tivmv ilvdi
Kai TTEpi ri Kal riviiiv rryii dTTodei^iv.
Met. iii. 2. emep vaaa cnroStiKTuerl
irtpi n inroKiipsvov Osdtpti rd Kad'
avrd avfiPe^riKora h tS>v koiviSv
oo^iiSv' Trepl ovv rh avrb yevog rd
(TvpfiijiriKora Kaff avrd rffQ airfiQ
koTi 9sti)pi](Tai Ik rdv airStv So^&v .
— Ibid. See Post. Anal. ii. 12.
SCIENTIFIC PRINCIPLES ARE ETERNAL. 51
would be possible, as will be shown, if Number were the genus
of Magnitude ; for Arithmetical and all scientific demonstration
always expresses its peculiar subject ; and unless the subject is
wholly or partly the same, the demonstration is in transferable
and incommunicable to any other genus : i for if the middle and
major are not homogeneous to the minor, they are accidental
attributes and unessential.
§ 2. Geometry, therefore, will not demonstrate that Con-
traries are simultaneously known ; nor that the product of two
cube numbers is a cube : nor will any- science establish a
theorem for another, unless they stand in the relation of genus
and species, as Geometry and Optics, Arithmetic and Harmonics.
Geometry will not even investigate aU attributes of Lines ; not
those which are unessential, and do not derive from her pecu-
liar and appropriate principles. It will not discuss whether the
straight line is the line of beauty, or whether it is contrary to
the circular ; these attributes not attaching to their particular
genus, but to something it holds in common with other genera.
CHAPTER VIII.*
SCIENTIFIC PRINCIPLES ARE ETERNAL.
§ 1. If the premisses of absolute demonstration and science
are commensurate, the conclusion must be eternal. Transient
' A dialectical proposition or proof 5i£ icat Iw' aXXo yivoQ. — Ibid, iregai
differs from a scientific in being ap- Tif yivu aX dpxal ical oiiS" i<l)apii6T-
plicable to several subject-matteTS. Tovaai. — Chap, xzxii.) ap/ioTreiv. —
The terms used by Aristotle to ex- (Soph. Elench. II. Also ibid. 20,
press this character are : furapai- where it is applied to Solution. tSv
vuv {oiiK tariv i? oXXow ykvovg fit- yap irapd ravTov Xoytitv ri av7~q
To^avTa SeX^ai. — Chap. vii. ti /tlX- Xvcrtc' avrri S" ovx ap/ioaei iiri ■jrdv-
\u 17 airoSu^ic lUTafiaiveiv. — Ibid.) rag. Sia^aivav (ou -ydp ^v i% dXXov
lUTOfipciv (Sia t6 lUTa^epo/uvov yevove «c aXXo ykvoe Sutfi^vai ra
tKaOTov iiv o/wiiug tlvai S^Xov. — Stuevvfieva. — Post. Anal. i. 23.)
Soph. Elench. 32. a-pog jroXXoie " This chapter appears misplaced
iaTi jUTOityKiiv. — Ibid. 11.) l^ap- as it interrupts the connexion be-
uoTTtiv {kir' oXXwv i^apiioTTOvaiv ol tween chapters vii. and ix. It might
\6yoi ov mjyytvtav. — Post. Anal, i, come before chapter vii.
9. ov yctp 3.V i^ripixoTTtv ij airoSii-
52 THERE IS NO UNIVERSAL SCIENCE.
and perishable attributes, therefore, being temporary and in-
commensurate, are objects of accidental, not absolute science
and demonstration. If you prove theit actual existence, your
minor premiss must be perishable and incommensurate, because
the conclusion is perishable and incommensurate. The perish-
able, if indemonstrable, is also indefinable ;' definition being
either the premiss of demonstration, or the conclusion, or the
whole demonstration dislocated. In investigating temporary
predicates, like the moon's eclipse, your conclusion must be
particular in order to be temporary : if it were universal, it
would be eternal.
CHAPTER IX.
THERE IS NO UNIVERSAL SCIENCE.
§ 1. If demonstrated predicates are essential, and the pre-
misses of demonstration peculiar to the subject, science is
something more than proof by true and indemonstrable and
immediate propositions. For such a proof, like Bryso's
squaring of the circle, may conclude by a cause that is not
peculiar to the subject, but attributable to other genera, and be
transferable to a heterogeneous matter. If the essence of the
subject and not an accident is the cause of your knowledge, the
demonstration is not transferable to another genus. Our know-
ledge of a predicate is merely accidental, unless we attribute it
to its essential subject, evolving it from the elements of its sub-
ject's essence ; as we know the attribute of containing angles
equal to two right angles from the elements of the essence of
that subject to which it is essential. That subject must again
be the essential predicate of an antecedent subject, and the
middle term and extremes are therefore always homogeneous.
§ 2. We know indeed Harmonic laws by Arithmetical proof,
and this knowledge is legitimate : for though the laws are
stated by an inferior and separate science, the subject-matter
being heterogeneous ; the proof is given by the higher science,
with whose subject the predicate is essentially connected. Even
' See book ii. chap. 9.
THERE IS NO UNIVERSAL SCIENCE. 53
in this case it appears that there is no absolute demonstration
except from appropriate principles: the appropriate principles
of Harmonic theorem being generic and Arithmetical.
§ 3. The peculiar principles of each particular genus are in-
demonstrable :^ else the principles of such demonstration would
be universal, and we should have one sole and universal science.
For if science is more perfect the more primary the causes from
which it deduces, a science deducing from uncaused and abso-
lutely antecedent causes would alone be perfect and absolute.
But demonstration is not transferable, except between genera
related like those of Harmonics and Arithmetic, and those of
Optics or Mechanics and Geometry.
To discriminate absolute science from unscientific belief is not
easy: for it is not easy to determine what knowledge is based
on the principles appropriate to the subject-matter. Deduction
from true and elementary propositions passes for science: but
besides this, the principles and conclusions ought to be homoge-
neous.2
' This, and in general the doctrine o Qtog, Nic. Eth. i. 6.), and self-
bf Appropriate principles, seems di- existent (xifpioTov ibid.), eternal and
rected against Plato, who apparently unchangeable (aBtVjjrov), and the
held that the principles of the par- absolute Best (ri 'Apiarov Iv ry
ticular sciences might be obtained ^vaii irday, Met. i. 2.): whereas
by deduction from the principles of the subject of Ethics, Virtue or Hap-
the primary science. See ch. xxxii. piness, is an attribute (axtftptoToi')
° We have here, apparently, the producible (jrpaKTbv i. e. Kivtiriv),
ground on which Aristotle differed and merely the relative Best (r6
from Plato as to the relation of tSv irpaKT&v apiarov). As they
Ethics {^povriine) to Metaphysics or are thus heterogeneous, it is irapos-
Natural Theology {ao^ia). The Su- sible to pass by scientific deduction
preme Good contemplated by the from the nature of the one to the
one is heterogeneous to the Supreme nature of the other. Ethics there-
Good contemplated by the other, fore cannot be, as Plato considered
That contemplated by Metaphysics (de Repub. 6.), a deduction from
is a substance (Iv rif ri ionv 'AyaQbv Theology.
[64]
CHAPTER X.
HYPOTHESES.
§ 1. First principles are indemonstrable propositions. They
are either the definition of the elementary, its combinations
and attributes, as Unity, Triangle, Curve ; or the affirmation of
the existence of the elementary, as unity and magnitude. The
existence of the compound and of the predicates must be esta-
blished in the conclusions.
§ 2. Of demonstrative principles some are peculiar to each
separate science ; as the definitions of Line and Curve to Qeom%-
try : others in an analogous, not an identical, form are common
to all sciences: as the principle, that if equals be taken from
equals, the remainders are equal. A particularized statement is
as useful as the most universal formula to a particular science.
We only want the specific form that refers to our own genus.
The Geometrical form of the axiom will suffice the geometrician,
the Arithmetical form the arithmetician.
§ 3. Among the peculiar principles science assumes, are
the existence and definition of the subject whose essential laws
she has to trace. Arithmetic assumes the existence and defini-
tion of Unity ; Geometry of points and lines. They further
assume the definition of the essential attributes — Arithmetic of
odd and even, square and cube; Geometry of angular, inclined,
incommensurate. The existence of the attributes is demon-
strated by the axioms and former conclusions.
§ 4. The same is true in Astronomy. For in all demonstrative
science there are three elements : the Subject, whose existence is
assumed, and whose essential laws are developed ; the Axioms,
which belong alike to every science; and the Attributes, of
which we assume the definition, and demonstrate the existence.
When any one of these is obvious, it will be neglected : if the
existence of the subject is obvious, an Hypothesis is not needed.
It is not equally necessary in Arithmetic and Chemistry. If the
definition of a predicate is obvious, it may be omitted. The
meaning in the axiom of subtracting equals from equals is too
HYPOTHESES.
55
plain for definition. But really there are always three elements ;
the subject, the attribute, and the proving canon.
§ 5. The Axiom, being a necessary truth and necessarily be-
lieved, is distinct from Hypothesis and from Petition or Postu-
late.^ I say necessarily believed, though some have attacked
the axiom ; for demonstration and syllogism depend on the men-
tal, not the spoken proposition. You may always assail the
expression, but not the thought.*
§ 6. What is capable of proof, but assumed without proof, if
believed by the learner, is, relatively to the learner, though not
absolutely, an Hypothesis ; if the learner has no belief or a
disbelief, it is a Petition : and this is the difierence. Petition is
an assumption opposed to the belief of the learner : or, still
wider, a demonstrable proposition assumed withoiit demon-
stration.
§ 7. Definition is distinct from Hypothesis, for it affirms no
existence. Definition needs only be understood, and this is not
' (to dS'cJ/ia) cipxf) awiroBsTog'
r]v ydp avayKoiov t\uv rbv otlovv
^wikvTa r&v ovrtov tovto ovk viro'
9iaiQ. — Met. iv. 3. From the in-
ferior evidence of the existential pro-
position some have said that all de-
monstrative science is hypothetical ;
this is not Aristotle's view, as he in-
cludes the hypothesis, or cateyforical
element, among the first principles
of Demonstration.
' OVK toTi yd,p avayKoiov, Utiq
Xiyii TavTa Kal viroXa/ijidvHv. —
Met. iv. 3. 'EipnriStiov ri avfi-
pijaetai' 17 /liv yap yXwrra dvk-
XiyKTog rijiiv larai, ri Si ^pvv oiiK
dviXeyKTog. — Thesetetus, % 29. It
was an artifice of the Sceptics to
profess not to see the evidence of
the Axiom ; then, if a proof of any
proposition was adduced, they said,
Before we can accept this proof, we
must have a criterion of its legiti-
macy J and before we accept a crite-
rion, we must have a proof of its
authority; and the legitimacy of
this prior proof must be guaranteed
by a prior criterion ; and so on ad
infinitum, (Sextus Empiricus.) As,
however, the perception of the Axiom
constitutes the reasoning faculty, not
to see its evidence would be not to
have the faculty of reasoning. Ari-
stotle calls the Sceptics stocks, (S/iot-
og yap (pvTif 6 toiovtoq. — Met. iv. 3.)
the Stoics called them stones, (diro-
\i9ti)ffig yap Iotl tov votjtikov orav
Tig irapaTiTayfiivog y pri iirivtinv
Totg ivapyiai. — Arrian, i. 5.) if they
could not see the force of the Axiom.
It is a mistake to attempt to demon-
strate the principle of demonstra-
tion, d^iovffi 5t Kai TOVTO diroSeiKvii-
vai Tivig Si diraiStvalav' iffTi yap
diraiStvaia Tb firj yivfiiOKUv, Tivbtv
SeX ZtitHv diroSei^iv, xal tivwv ov
StX. — Met. iv. 4.
56 AXIOM OF CONTRADICTION.
Hypothesis, unless sensation is Hypothesis ; for Hypothesis is
a premiss whose existence produces a conclusion. The geo-
meter is not guilty of a false Hypothesis, as some say, when he
calls a line straight, or a foot in length, that is not straight nor
a foot in length. Not the straightness nor length of this line,
but that which it represents, is the ground of his conclusion.
Petition and Hypothesis are either universal or particular ;
Definition is neither.
CHAPTER XL
SYLLOGISM DEPENDS ON THE AXIOM OF CONTRADICTION,
§ 1. The existence of Ideas, or unities separable from many,
is not indispensable to demonstration ; which only requires the
existence of classes, or unities predicable of many. Unless one
and the same thing is predicable univocally of many, there
could be no demonstration, for there could be no commensurate
middle.
§ 2. That of two contradictory" predicates one must be false,
is never expressed in demonstration, but implied in all direct
proof.i When we syllogize, we assume that the Major is truly
affirmed of the Middle, and not truly denied, without caring
whether the Middle can be truly denied of the Major. And so
with respect to the Middle and Minor. For if we assume that
all Man is Animal, and not not-animal ; it will be true that
Callias is Animal, and not not-animal ; even though not-Callias
be also Man, and not-man be also Animal. For the conclusion
is not impaired though the Major be incommensurate to the
Middle, and the Middle incommensurate to the Minor.
§ 3. The principle that one or the other of two contradicto-
ries must be true, is assumed in indirect proof; not in its com-
' The principle of syllogism, the argument proposed. See Post. Anal.
dictum de omni et nulla, is not em- ii. 6. oirf Iv avWoyuTfuf Xa/ijidve-
ployed as a premiss : if, however, rai ri lari rh avXKeKoyiaBaC dXXdi
the conclusiveness of an argument is irpbg rbv dfifia^rirmivTa d avSXi-
challenged, the pi-inciple may be Xoyiarai ri fxr) tovto, dvavrdv Set,
expressed and compared with the brc tovto yap ifiv ayXKoyta/ide.
PECULIARITIES OF SCIENCE. 67
mensurate form, but so far as it is applicable to a particular
matter.
§ 4. The common principles express neither the subject nor
the attribute, but are the canons of demonstration ; and are the
common property of the particular sciences, of Dialectics, and
of (Metaphysics,^ or) whatever science it is which makes a
commensurate investigation of these propositions ; Of two con-
tradictories one or the other must be true ; Equals, from which
equals are subtracted, have equal remainders ; and the like.
Dialectics has no peculiar and definite premisses, nor a single
subject-matter, or it would not accept the opponent's proposir
tions.* You cannot be indiiFerent to the concessions, if you
wish to demonstrate: for, when treating of syllogism, we
showed that opposite premisses wUl not furnish the same con-
clusion.
CHAPTER XII.
PECULIARITIES OF SCIENCE,
§ 1. A syllogistic question is the proposition of a necessary
alternative, and as propositions are peculiar to each science, a
question may be inappropriate to a given science. A geome-
trician or physiologist may be asked an ungeometrical or un-
pbysiological question. Only the premiss of a Geometrical con-
clusion, or of a conclusion, like an Optical theorem, that is
drawn from Geometrical premisses, is Geometrical : and such a
question the geometrician is bound to solve by the principles
' MetaphyBicB is not mentioned in viUvoilk ykvovg Mg rivog, chap, xi.)
the text, but the investigation of the That it has no appropriate prin-
Axioms is assigned to this science, ciples : (spdirti/ia iirurrriiioviKbv iH
Met. iv. 3 ; also Met. xi. 4. tvel Sk Hv o icaff aKceuTriv oiKnog yiyirai
6 /laOr/fianKbg xpnrai roig KOivoig avXKoyiaiiog, chap, xii.)
iSiag, kui T&g tovtiiiv apx^S ^v tJij That it is not confined to defini-
Otaipnaai rrjg irp&Ttjg ^CKoao^iag. tions, but employs accidental pre-
' From this and the following misses: (oiSkv av/iPePtiKbg Xa/iPA-
chapter it appears that Dialectics vovai to, /laOriiiaTa, aWd Kal roirif
has no definite subject-matter : (17 Suupkpovm tUv Iv roig SiaKoyoig,
Si jiaXcicruci) oiiK ttrnv iipiafAviitv ti- dXK' bpwfiovg. — Ibid.)
68 PECULIARITIES OF SCIENCE.
and conclusions of Geometry. As geometrician, he is not
bound to answer an opponent who questions the principles of
Geometry.* The professor of a particular science is not bound
to answer all questions indiscriminately, but only those which
fall within the province of his science. In controversy with a
geometer only conclusions from Geometrical premisses are legi-
timate ; or, if they refute him, they only refute him accidentally,
and not as a geometrician. A Geometrical controversy should
be conducted before a tribunal of geometers ; else an ungeome-
trical argument will pass without detection : and so in other
sciences.
§ 2. If some problems are ungeometrical and do not belong
to the geometer, what ignorance is Geometrical, and when does
it affect the pretensions of the geometer ? and, in general, what
kind of ignorance affects our pretensions to any particular sci-
ence ? Is that syllogism which is constructed of premisses
contradictory to the true, the ^ Geometrical paralogism, ungeo-
metrical ? or rather, the syllogism belonging to an extraneous
science — ^for instance. Music ? The answer to this is, that un-
geometrical, like unrhythmical, is equivocal ; implying either the
absence or the badness of Geometrical character. To suppose
that parallel lines can meet, is in the first sense Geometrical, in
the other ungeometrical. Ignorance founded on principles un-
geometrical in the latter sense is inconsistent with pretensions
to Geometrical science.
§ 3. In Mathematics, logical fallacies are not so practicable as
elsewhere. Two terms, the minor and middle, ought to be dis-
tributed ; the major may be undistributed. In Mathematics the
fulfilment of these conditions is more obvious than in naked ar-
gument, as the diagrams submit them to ocular perception.
Is every circle a figure ? Is a poem a circle ? The diagram be-
trays the equivocation.
The subject of discussion must not itself be brought as
' Tif ytufiirpy Ovk en \6yog kari i;\);j .... Xeivirai roivov rf/v rrpo-
*pbs rhv dviKovTa rag dpx^S; «^^' Ku/ievtiv ^iKoao^iav iripl airSv rriv
■iJToi trepas iinaTi]jii\g fi traaSiv Kot- (TKtif/iv nouXoBai.^—Met. ii. 1 .
v^g, — Phys, Ausc. i. 3. diropiiatii ° i. e. the Pseudographema. — See
Tig av TToiaC IvTiv imarriliriQ TO iia- Soph. Elench, 11.
TTop^ffttt TTipi Trjg rS)V fiaBiijiariKi/iv
PECULIARITIES OF SCIENCE. 69
enstasis against an inductive proposition : for as a proposition
must be general, or it would not be commensurate, so must an
enstasis be.^ For every enstasis is a proposition ; ■ every enstasis
may become a premiss in dialectical or demonstrative syllogism.
An argument is illogical when the middle is the predicate of
both terms it is intended to connect : as Ceeneus argues, that
fire increases in a geometrical proportion, because both fire and
this proportion augment with great rapidity. The conclusion
would follow, if fire developed in the most rapidly augmenting
proportion, and such proportion were geometrical.
§ 4. Sometimes the premisses, though inconclusive in their
original form, may be remodelled so as to furnish a legitimate
conclusion. If true conclusions never resulted from false pre-
misses, they would be reciprocally demonstrable, and it would
be easy to analyze a theorem into its principles. This recipro-
cation is more common in Science than in Dialectics, for the pre-
misses of the former are never accidents, but definitions.
§ 5. The demonstrative chain grows by apposition of terms,
not by interposition. For instance : A is predicated of B, and
B of C, and C of D, ad infinitum.'^ Or it takes two directions :
if, for example, A is predicated of B and D, and these are re-
spectively predicated of C and E : A representing number finite
or infinite : B finite odd number : D finite even number : C a
particular odd number : E a particular even number : we have
two lines of predication. A, B, C, and A, D, E.
' The drift of this is obscure : it ' Synthetical reasoning uses no
may mean : in Geometry the subject premisses between whose extremes a
of discussion itself is present, and middle can be interposed ; proof is
exposes any equivocation : but in the interposition of middles between
Dialectics it is not allowed to adduce the extremes of a problem, rip yAp
the subject of discussion itself as an ivrbg ifi^dSXiaOai 'opov aXX' ov Tif
objection against a proposition, but ■jrpoakafi.^avtaBai awoScUvvTai to
we must find a similar case that falls airoSeiKvi/ievov, chap. xxii. av^irai
under the same universal. See Top. is used for the deduction of a given
viii. 2. d%uiiTiov Tag- ivardirug fiv conclusion, chap. xiv.
iw' airov row irpoTCivofuvov ijikpuv.
[60 ]
CHAPTER XIII.
FACT AND REASONED FACT.
§ 1. Knowledge of a fact is distinct from knowledge of its
reason; and if it belongs to the same science, presents two
varieties. Either the premisses from which we conclude are not
immediate, and cannot disclose the primary cause ; or, though
immediate, they do not conclude from the cause, but from its
reciprocating and more evident effect : for an effect is often more
evident, and supplies a middle term for the demonstration of
its reciprocating cause.
§ 2. The proximity of the planets may be proved by the
absence of scintilla tion.^ Let C represent the planets, B non-
' The following examples are
taken from Mr. Whewell's Philoso-
phy of the Inductive Sciences. " It is
inferred that the earth is a globe,
because we find that as we travel
to the north, the apparent pole of
the heavenly motions, and the con-
stellations which are near it, seem to
mount higher, and as we proceed
southwards they descend. Again,
if we proceed from two difierent
points considerably to the east and
west of each other, and travel di-
rectly northwards from each, as
from the south of Spain to the north
of Scotland, and from Greece to
Scandinavia, these two north and
Eouth lines will be much nearer to
each other in their northern than in
their southern parts. These and
similar facts are seen to be consistent
with a convex surface of the earth,
and with no other." — Bk. ii. ch.6.
Here, as the convergence of meri-
dians towards the north, and the
visible descent of the north pole of
the heavens as we travel south, are
made the middle term, and the glo-
bular form of the earth the major,
the reasoning is analytical or in.)
ductive, and the conclusion merely
a fact : if the middle and major
changed places, the conclusion would
be a reasoned fact.
Again, from the risings and set-
tings and eclipses of the moon, it is
inferred that she moves in an ellipse,
with variable axis and eccentricity';
and this is explained by supposing
that she is attracted by the earth
and sun inversely as the squares of
the distance. — See Inductive Table
of Astronomy.
The conclusion of the first syllo-
gism is the movement of the moon ;
of the second, the forces by which
this movement is produced ; and
both are fact-conclusions. If we
started from the forces we might
deduce the movement, and from the
FACT AND REASONED FACT. 61
scintillation, and A proximity. B is true of C, and by induc-
tion or sense we know that A is true of B, therefore A is true
of C. "We have now demonstrated the fact of their proximity,
without the reason ; for non-scintillation is the effect, not the
cause, of proximity. Invert the proof, and you have a demon-
stration by the reason. Let the middle B represent proximity,
and the major A non-scintillation, then the middle, by which we
conclude A of 0, is the primary cause, and we have a demon-
stration by the reason. So if, from the moon's waxing and
waning, we conclude that her shape is spherical, we prove a
fact ; if from her sphericity we infer the phsenomena of her
waxing and waning, we prove by the reason ; for her spherical
shape causes the phaenomena of her waxing and waning.
§ 3. The other case of fact-conclusion occurs when the
middle and major do not reciprocate ; then, if the effect is more
notorious, the fact may be proved without the reason ; and
when the middle is not intermediate, but exterior to the ex-
tremes, as in the second figure, then we can prove the fact,
though ignorant of the reason.^ We do not assign the cause of
a wall's non-respiration, when we say it is not an animal ; for
the animal character is not the cause of respiration. For if a
negative is the cause of a predicate's absence, the affirmative is
the cause of its presence : if the distemperature of heat and
cold is the cause of sickness, then temperature is the cause of
health : and if an affirmative is the cause of a predicate's pre-
sence, the negative must be the cause of its absence. In the
above instance this condition was wanting ; the animal charac-
ter does not involve the presence of respiration. The inference
movement the phsenomena, and these the basis of the inductive inference
would be reasoned conclusions. are the conclusion of the train of
Again, the ebb and flow of the deduction. And in this manner the
tides may be made either a middle deduction establishes the induction,
term to prove the attraction of the The principle which we gather from
sea by the son and moon, or a ma- the facts is true, because the facts
jor term to be proved by this attrac- can be derived from it by rigorous
tion. — Ibid. demonstration. Induction moves
" The doctrine which is the hypo- ^upwards, and deduction downwards,
thesis of the deductive reasoning is on the same stair." — Book ii. 6.
the Inference of the inductive pro- ' IKot is equivalent to dviuTepu. —
cess. The special facts which are Sea chap, xxiii.
62 FACT AND REASONED FACT.
■was made in the second figure : All that respires is animal ; a
wall is not animal ; therefore a wall has no respiration. Similar
to this are far-fetched reasons, as that of Anacharsis, who said
there were no flute-players in Scythia because there were no
vines.
§ 4. Within the same science, and with reference to the posi-
tion of the middle term, the sj'Uogism of fact and the syllogism
of reason thus difier. The fact also differs from the reason, as
belonging to a difierent science, having the relation of Optics to
Geometry, Mechanics to Stereometry, Harmonics to Arithmetic,
Celestial Pheenomena to Astronomy. Such sciences are not
always distinguished by name : as Mathematical and Nautical
Astronomy ; Mathematical and JEsthetical Harmonics. The
fact belongs to the ^sthetical, the reason to the Mathematical
branch. . The professor of the latter, though he could give the
causal demonstration, is often ignorant of the fact : as we are
often ignorant of phsenomena, when we know a universal law, if
we have not traced it through all its manifestations. This hap-
pens when the specific element connected with an attribute, and
whose connexion is expressed in the law, is mixed in the phae-
nomenon with a mass of other elements : for Mathematics sepa-
rate the element they examine ; which, though insulated in the
science, perhaps never exists in nature except in combination.^
As Geometry is related to Optics, so are Optics to the theory
' On the subject-matter of Mathe- rpeif civ elev 'biXoao^iai Beiaptinical,
matics see Metaph. xiii. 3 ; Post. MaOrifianier), iumic)), QeoXoyiKt]' oil
Anal. i. 18. The following is a divi- yap adrfKov in, n vov rh QiXov
sion of the sciences : ») diraaa Sid- vvapx^h ^^ ''? rotavry fvaii inrap-
voia ri lipaKTiKt] rj TloLrfTiKri ^ Qeo}- y^ei' /cat Tyv TifubtTOLTiiv Sei inpl t6
prjTiKri . . . . d Sk n larlv Sikiv^tov riiwirarov ykvog tlvai. — Met. vi. 8.
Kal aiStov Kai ^wpiffrAj/, ^avtphv '6ti See also Met. xi. 3, 4, and 7. i) Bk
BeioptiTiK^S rb yvSivai' ov pi/vToi ^v- MaOtnianKr] deoipijnK^ jiev Kal vspi
(TLKTJg ye, nepl kivtjt&v yap Ttvwv ij fikvovrd rig avrfj, aXV ov ^^wptffra*
4>w(riKi7, ovSh MaBrjpaTiKfiQ, aSXd ei S" inrdpxu Tig oiiaia x'^pi^T^ "ai
irporkpag d/ifoXv. 'H jiiv yap *«- dxivfirog, hirep inipaaojjitBa Seikvv-
BiK-q irepi axcipwrra piv, dW ovk vai, ivravQa &v ciij irov Kai t& BiTov.
dxivTjTa' Trig ^^ Ma9)ipanK^e ivia SijXov Toivvv on Tp'ia ykvri tS)v 6eo)-
Trepi dxivriTa /lev, ov xiapiard le pi/riKoiv iiriffrij/ioiv Ian, ^vaiKti,
iauig, dXK' iig iv v\y ri Si Ilpiinj MadtjpaTiKr), 0£o\oyiK^.
Kai TTfpi i^wpKTrd Kai dKivr)Ta' iiari
THE FIRST FIGURE IS MOST SCIENTIFIC. 63
of the Rainbow. The explanation strictly belongs to Optics :
the facts to Physical science. Many sciences not subordinate
are in particular points thus related. The fact, that circular
wounds are slow to heal, belongs to the Physician; the expla-
nation to the Geometer.
CHAPTER XIV.
THE FIRST FIGURE IS MOST SCIENTIFIC.
§ I . Of all the figures the first is most employed in science.
It is employed by all the mathematical sciences. Arithmetic,
Geometry, Optics, for instance r and a reasoned conclusion, the
most characteristic point of science, is generally if not univer-
sally drawn in this figure.
Secondly, it is the only one adapted for establishing a defini-
tion, which is universal and affirmative, the conclusions of the
second and third being negative and particular.
Thirdly, the intercalation of more and more elementary laws,
and finally of the immediate, by which the premisses of the lat-
ter figures are deduced, must take place in the first figure.' The
first is self-sufS.cient, and appears on these accounts to play the
chief part in science.
1 Deduction is called condensa- All C is D.
tion, (KarairvKvovTai,) because it .'.AUCisE.
consists of the interposition of mid- And
die terms. The proposition, all A is All B is C.
£, is thus deduced : — All A is B.
AllCisE. .-.AUAisC.
All A is C. The deduction is complete when
-•.All A is E. all the premisses, AB, BC, CD,
Both of these premisses may be D E, are immediate propositions,
thus deduced : — dd rb fiiaov irvKvovrai 'io)Q dSiat-
AU D is E. pira yivrirai Kai cv, chap. XXIII.
[64 ]
CHAPTER XV.
NEGATIVE PEOPOSITIONS MAY BE INDEMONSTRABLE.
The proposition, B is not A, as well as the proposition, B is
A, may be an atomic truth. A proposition is an atom or indi-
visible, whose terms are divided by no intermediate link, and
connected or disconnected by no foreign cause.
If either A, or B, or both, have a genus, the disjunction of A
and B cannot be primary. For, if C is the genus of A, it per-
haps is not the genus of B : then, because A is C, and B is
not C, we may infer that B is not A. Or if D were a genus of
B, so that all B were D, and no D were A, we might infer that
no B is A. And similarly, if both B and A have a genus. The
possibility that the genus of A should not be a genus of B, or
the genus of B not a genus of A, is clear from the contra-dis-
tinguished categories or orders. If nothing in the category A,
C, D, is predicable of any thing in the category B, E, F, and G
in the first group is genus of A, it cannot be genus of B, or the
groups would not be mutually exclusive; and similarly if B had
a genus.
If neither has a genus, and B is not A, the proposition is an
atomic negative. Were there a middle term and proof, one of
them must have a genus : for the proof must fall into the first
or second figure. If in the first, B has the genus, for the minor
premiss of this figure must be affirmative : if in the second, one
or the other must have the genus, for either premiss may be
negative, but not both.
Under these conditions a negative proposition may be indivi-
sible or atomic.
[65 ]
CHAPTER XVI.
ERROR IN PRINCIPLE.
§ 1. Ignorance, that is not merely the negative but the eon-
trary of knowledge, is either direct or concluded ; and either of
mediate or of immediate propositions. Ignorance of immediate
or primary propositions, whether aiErmative or negative, if a
direct belief, admits of no varieties : if a concluded error, it
may arise under several conditions.
§ 2. Let the proposition, no B is A, be an indivisible or
atomic truth. If you conclude that all B is A, by a middle
term C, you are deceived by deduction : and either both, or only
one of your premisses,
all C is A
all B is C,
may be false. Both may be false : for it is possible that the
statement, all C is A, is false ; and, as the proposition, no B is
A, is primary, and B can therefore have no genus, the state-
ment, all B is C, is also false.
Or one of the premisses may be true : but this can only be
the major, aU C is A. The minor, all B is C, must be false ;
for, if the proposition, no B is A, is primary, B can have no
genus. The major, all C is A, -may- be true; for the propo-
sitions,^
all C is A
no B is A,
whether mediate or immediate, are quite consistent with the
proposition, no B is C.
§ 3. This is the only manner in which we can conclude a
false affirmative, for only the first figure concludes an afiirmative
universal. A false negative may be drawn either in the first" or
' This passage and another in the where KartiyopeXaBai and virapx^iv
following chapter {iyxiapii yip ri are used generically of affirmative
A irXtiomv virapx^iv S, oiie ianv and negative propositions.
wTraWijXo) are the only places
K
66 ERROR IN PRINCIPLE.
in the second figure. Let us examine under how many condi-
tions a false conclusion, no B is A, may be drawn in the first
figure.
Both the premisses,
no C is A
all B is C,
may he false : for the assumption, that all C is A, and no B is
C, does not contravene the hypothesis, that all B is A.
Or one or the other indiscriminately may be false : The major,
no C is A, may be true ; and then the minor, all B is C, must be
false : for, firstly, the propositions,
all B is A
all B is C,
would give the conclusion, some C is A, which contradicts the
major we have just assumed to be true ; and, secondly, the
premisses,
no C is A
all B is C,
give the conclusion, no B is A, which contradicts the hypothesis.
Or the minor, all B is C, may be true ; and then the major,
no C is A, must be false : for, from the hypothesis and minor,
all B is A
all B is C,
it follows that some C is A, and therefore the major, no C is A,
is false.
In the first figure, then, a false conclusion may proceed from
either one or two false premisses.
§ 4. If the false conclusion, no B is A, is drawn in the
second figure, the premisses cannot both be wholly false or
contrary to the truth. If all B is A, no middle term can be
universally affirmed of one extreme, and universally denied of
the other: for the false conclusion, no B is A, tnust result from
such premisses. But they cannot both be contrary to the truth ;
for then the contraries of both ought to be true propositions ;
but we should again have a middle term universally denied of
one extreme, and universally afiirmed of the other.
§ 5. Both premisses may be partly false or contradictory to
the truth. Whether the premisses are, all A is C, and no B is
ERROR IN PRINCIPLE. 67
C ; or, no A is C, and no B is C ; we may suppose them both
contradictory to the truth, without contravening the hypothesis,
all B is A.
§ 6. Either premiss singly may be contrary to the truth.
Let the premisses be,
all A is C
no B is C ;
then, if the major is true, we have the true propositions,
all A is C
all B is A;
so that the minor,
no B is C,
is contrary to the truth.
Or, if the minor is true, we have the premisses,
no B is C
all B is A;
from which it follows that some A is not C ; and therefore the
major, all A is C, is contradictory to the truth, and may be
contrary.
Or, let the premisses be,
no A is C
all B is C;
then, if the major is true, we have the propositions,
no A is C
all B is A J
from which it follows that the minor, all B is C, is contrary to
the truth.
Or, if the minor is true', then we have the propositions,
all B is C
all B is A,
which give the conclusion, some A is C : therefore the major,
no A is C, is contradictory to the truth, and' may be contrary.
An atomic or elementary error may therefore result from one
or from two erroneous premisses.
[68]
CHAPTER XVII.
ORIGIN OF ERROK IN DEMONSTRABLE PROPOSITIONS.
§ 1. With respect to mediate or deducible propositions, aflirm-
ative or negative, if the middle by which they are falsely con-
cluded is appropriate, both premisses cannot be fake, but only
the major. The appropriate middle is that by which the truth
might be concluded. Let the true conclusion, all B is A, be
deducible from the middle C. The minor premiss must always
be affirmative and true ; if it were negative, there would be no
conclusion : but the major may be false, for, converted into its
contrary, it gives a contrary conclusion.*
§ 2. When the true premisses are,
' ' ' all D is A ■
- all B is D;
where the middle D is inappropriate, and taken from a
distinct category; we leave a conclusion if we change the
quality of the major, but not if we change the quality of the
minor : so that the one must always be true, the other always
false : and this case resembles that of the appropriate middle.
§ 3. Supposing the true premisses to be,
all t) is A
no B is D,
both .premisses of our deduction must be false: for we must
change the quality of both in order to make a syllogism : we
must assume,
no D is A
all B is D J
both which propositions are false.
' avnaTpofii here means change signifies the substitution of the con-
of quality; in Prior. Anal. ii. 8, it elusion for one of the premisses.
ORIGIN OF ERROR. 69
§ 4. In this last syllogism, if the major is true, the minor
must be false ; for it leads to the conclusion, no B is A, which
is false by hypothesis.
§ 5. When the erroneous conclusion is in the second figure,
both premisses cannot be wholly false or contrary to the truth :
for, as we observed before, when all B is A, no middle can be
universally affirmed of the one extreme, and universally denied
of the other ; but either singly may be contrary to the truth.
If the true propositions are
all A is C
all B is C;
and we assume the premisses,
all A is C
no B is C; '
the major premiss is true, and the minor false : if we assume
the premisses,
aU B is C
no A is C :
the minor is true, and the major false.
When the conclusion is negative, these are the sources of
error.
§ 6. When the conclusion is affirmative, and drawn from the
appropriate middle, both premisses cannot be false, for the
minor must be affirmative to give any conclusion ; so that the
error must be in the major : for this is the only premiss whose
contrary affords a conclusion.
§ 7. Similarly, if the middle be inappropriate and heteroge-
neous, as we observed in the case of the negative conclusion,
the minor cannot be converted into its contrary, but the major
can : and the deception is the same as when the middle is ap-
propriate and homogeneous.
§ 8. When all D, the inappropriate middle, is A, our major
premiss, all D is A, is true, and the minor, all B is D, is false.
For it does not follow from the propositions,
all D is A
no B is A,
that all B is D.
70 NEGATIVE IGNORANCE.
§ 9. If no D is A, our major premiss, being affirmative, is
false ; while the minor» all B is D, may be either true or false.
While no B is A, it may be true that no D is A, and all B is
D : for example ; music is a science, and neither music nor
science is an animal : or, it may be true that no D is A, and
no B is D.
If, then the major premiss is negative, one or both the pre-
misses may be false.
We have seen in how many ways it is possible to be misled
either in demonstrable or in indemonstrable propositions.
CHAPTER XVIII.
NEGATIVE IGNORANCE.
If man has lost any sense, he has lost a corresponding science,
now unattainable. We acquire knowledge by induction or de-
monstration, the one based on phsenomena, the other on laws,
which are only discoverable by induction.
Even the materials of mathematics are furnished by induc-
tion;' which shews us throughout nature certain attributes,
which, though not self-existent and substantive, are insulable
in thought. The cognizance of phsenomena belongs to sense,
not to reason. Sense, then, is indispensable to induction, and
induction to discovery of the law.
CHAPTER XIX.
ABE ANY TRUTHS IN THEIR OWN NATURE
INDEMONSTRABLE ?
§ 1. AH deduction involves three terms, and either connects
a predicate A with a subject C, by predicating A of B, and B of
' o fiaBtiitanKbg Trepi rd k^ A^ai- aWag aiaOtiTdg ivavTiiaasiQ' fiovov
peacue rrjv dewpiav irouirai' irepi- Sk KaTaKeiirn rb iroabv Kai am/ex^^j
eXiav ydip wdvra rd alaOtjtd dciujoct, rfiv fikv k^' ev Tutv S' k-jrl Svo twv
olav jSapoe Kai Kovf 6Ti]Ta Kai axXt)- S" kjri rpla, Kai r<4 iraSij rd tovtuv,
poTijra Kai Toivavr'wv, In Sk Kai y itoaa. kari Kai avvixd Kai oh kuO'
6fpn6TtjTa Kai ypvxportira Kai rag 'irepSv ri, Beiapci. — Met. xi. 3.
LIMIT OF ANALYSIS. 71
C ; or disconnects them by ascribing a predicate to the one and
withholding it from the other. Such statements are the ele-
ments and hypotheses of deduction. We condade that A is
predicated of C by the middle B ; and that A is predicated of B
by some other middle ; and that B is predicated of C by another.
Dialectics only aiming at belief, credibility, as far as circum-
stances allow, is the only requisite of its premisses. If a middle
term between A and B is credible, though not real, it is suffi-
cient for dialectical proof, but not for science.
When we predicate whiteness of man, the predication is es-
sential : whiteness is not ascribed to man, because man is
ascribed to any other substance.^^ When we predicate man of
whiteness, the predication is accidental : man is ascribed to the
whiteness, because the whiteness is ascribed to a man,
§ 2. Let C be the attribute of no subject, but the primary
subject of B, without any intermediate ; and let B be the pri-
mary subject of F, and F the primary subject of E : must such
a series terminate, or is it illimitable ?
§ 3. Again, if there is no essential predicate of A, and A is a
primary predicate of H, with no antecedent intermediate ; and
H of G, and G of B ; must such a series terminate, or may this
too be illimitable ?
This question differs from the former : the former asked, if
we begin from a primary subject, can we go upwards along an
illimitable series? The second, if we begin from a primary
predicate, can we go downwards along an illimitable series ?
§ 4. Again, Lf the extremes are fixed, can the intermediate
links be infinite ? When B is intermediate between A and C,
and others between A and B, and others between these ; can
this intercalation be endless ? This is to ask, is there any end
to demonstration? is everything demonstrable, or are the con-
necting intermediates finite ?
§ 5. The same question arises in negative syllogisms and
propositions. When no B is A, A is either denied primarily of
< This kind of essential or proper predication mentioned in chap. iv.
predication, which occurs again at and at the end of chap. xxil. which
the beginning of chap. xxii. must is characteristic of science, and is only
not he confounded with the essential one species of proper predication.
72 LIMIT OF ANALYSIS.
B ; or antecedently of some other term G, which is predicated
of all B ; and either primarily of G, or antecedently of some
other term H. There is either an endless series of terms of
which A is antecedently denied, or there is a primary term that
ends the series.
§ 6. In a reciprocating series there can he no primary nor
ultimate term ; for there is no antecedence nor subsequence,
even though both the ascending and the descending series are
limitless ; their reciprocation, however, may be dissimilar, giv-
ing- sometimes an essential, and sometimes an accidental pre-
dicate.
CHAPTER XX.
INTERMEDIATES OF GIVEN EXTREMES ARE FINITE.
§ 1. If the series of ascending or more universal predicates,
and descending or more particular subjects, is limited in both
directions, the number of intermediates must be finite. If the
terms interposed between the extremes of the proposition, F is
A, were innumerable, we might start from F, and travel up an
endless succession of predicates without reaching A ; or start
from A, and travel down an endless succession of subjects,
without reaching F. This by hypothesis is impossible : the
intervening links between F and A are therefore finite.
§ 2. It is equally impossible that some should touch and be
undivided, and others severed by an impassable chasm. Select
any intervening term whatever, and the number of intermediates
that divide it from A and F must either be finite or infinite.
Where the chasm occurs is immaterial. The hypothesis is
violated, if any term is severed by an infinite series from either
extreme.
CHAPTER XXI.
NEGATIVE PROPOSITIONS.
§ 1. If the retrogression of subjects and progression of pre-
dicates is limited in the analysis of affirmative propositions, it
must be so in the analysis of negative.
LIMIT OF ANALYSIS. 73
Let us examine the proof of a negative conclusion in the
three figures ; and assume that, ia affirmative propositions, we
cannot progress from a primary subject, nor retrogress from
an ultimate predicate, without arriving at a limit.
§ 2. If we prove the negative, no C is A, in the first figure,
by the premisses,
no B is A
all C is B,
the number of intercalated terms in the minor interval or pro-
position, C is B, is by hypothesis finite ; for this interval is
always affirmative. The major may be proved by the antece-
dent premisses,
no D is A
all B is D;
and this major by the antecedent premisses,
no E is A
all D is E:
so that every antecedent proof adds a higher predicate of C ;
and,^^ as their progression is by hypothesis limited, the subjects
of A must be also limited ; and there must be some term of
which A is primarily denied.
§ 3. In the second figure, if we prove the conclusion, no C is
A, by the premisses,
all A is B
no C is B^
the minor premiss may either be proved in the first or in the
second figure : let us prove it in the second ; and we require
the premisses,
all B is D
no C is D :
' Siar iird n lirt to avw "laraTai the line from A down to B. In the
bibe, KoX n liri rb kutui arrjatTai. rj Tauchnitz edition the avia and icdrw
M rb avw bSoe is the line of terms are transposed,
from B up to A ; »; etti rb kuto) is
li
74 LIMIT OF ANALYSIS.
if we again prove the minor, we require tlie premisses,
all D is E
no C is E :
so that every antecedent proof adds a higher predicate of A ;
and, if these are limited, the antecedent negatives are also
limited.!
§ 4. In the third figure, if we prove the conclusion, some C
is not A, by the premisses,
some B is not C
aU B is A:
the major premiss may either be proved in the former figures,
in which we saw the progression was limited ; or, if we prove it
in the third, we require the premisses,
some D is not C
all D is B:
and to prove this major, we require the premisses,
some E is not C
all E is D:
so that every antecedent proof adds a lower subject of A; and
therefore, as the retrogression of affirmative subjects is as-
sumed to be limited, the retrogression of negative subjects is
also limited.
§ 5. As, then, the number of proofs in each figure is limited,
and the number of figures is limited ; and as the product of
two finite numbers is finite ; the number of antecedent nega-
' The syllogisms examined are in and this major by the premisses,
Camestres ; if we examine them in no D is E
Cesare, the result is slightly differ- all B is E.
ent. We may prove the negative, From which it appears that the de-
no C is A, by the premisses, duction in Cesare does not always
no A is B add"a higher predicate of the major
all C is B, term, as in Camestres, but alternately
the major may be proved by the pre- a higher predicate of the minor and
misses, major,
no B is D
all A is D ;
LIMIT OF ANALYSIS. 73
tives wUl be finite, even though the conclusion should be
drawn in every figure.
If, then, the succession of subjects and predicates is limited
in the analysis of an affirmative proposition, it is limited in the
analysis of a negative.
CHAPTER XXII.
THE TRAINS OF PREDICATION ARE FINITE.
§ 1. First let us give a dialectical proof.
Predicates that compose the essential character must be
finite : else, as infinite elements could not be enumerated, such
character would be indefinable.
Before we can complete this proof we must make some pre-
liminary remarks.
§ 2. Predication is essential or proper, when I afiirm that
wood is white, or that a man walks. Wood is the subject of
whiteness : whiteness is an attribute possessed by wood or a
species of wood, not by another subject to which wood is also
ascribed.
Predication is accidental or improper, when I afiirm that the
white is wood, or that the white is musical. White is not the
subject of wood, wood is not an attribute ascribed to white or
to a species of white, but is a subject to which the attribute
whiteness is ascribed.
When I affirm that the white is musical, white is not the
subject of musical ; musical is not an attribute ascribed to
white nor to a species of white, but to man, a subject to which
the attribute whiteness is also ascribed.
§ 3. The predicates that enter demonstration are proper, not
accidental, and fall under the categories of substance, quality,
quantity, relation, action, passion, place, or time.
When substance is predicated, the subject is either the pre-
dicate or a species of the predicate, as when animal is predi-
cated of man.
When accident is predicated, it is neither identical with the
subject, nor its genus : as white is predicated of man.
No accident can exist but by inherence in a substance. The
Platonic Ideas are imaginary, and, even if they existed, would
76 LIMIT OF ANALYSIS.
be nothing to our purpose, not being concerned in demonstra-
tion.
§ 4. If A is a quality of B, B cannot be a quality of A, and
they cannot precipitate with absolute predication.
Such predication cannot be circular or reciprocal. If the
terms reciprocate as genera ; firstly, no essence would be de-
finable, for we could not exhaust an infinite series of genera ;
secondly, a genus would be a species of itself.
If the terms reciprocate as substance and accident, their pre-
dication is only accidental.
§ 5. Rectilinear predication cannot proceed without a limit.*
For the predicates are either substantive genera, and this series
we know to be finite ; or they are accidents, essential or unes-
sential. Every accident inheres in some term of the substan-
tive succession : their descending or subject series, therefore, is
limited by the limit of this succession : and, as their genera are
finite like those of substance, their ascending or predicate series
is also limited. The scale, therefore, has both a basis or pri-
mary subject, and an apex or ultimate predicate.
§ 6. Another dialectical proof is as follows : antecedent pre-
dicates make a proposition demonstrable ; and the demonstrable
cannot be apprehended better than by knowledge, and cannot
be known without demonstration. If the antecedents are nei-
ther known nor apprehended better than if they were known,
the consequents cannot be the objects of knowledge. The
number therefore of intermediate predicates must be limited, if
demonstration is categorical, and not merely hypothetical. If
the succession of higher predicates is unlimited, every truth is
demonstrable, but, as an endless preceding series has to be
passed, cannot be demonstrated ; and, as we do not apprehend
them with any thing better than knowledge, our science is not
categorical, but merely hypothetical.
§ 7. These proofs are dialectical -.^ a scientific and shorter
' aWd lii Otis' (ig rb avo) avtipa and most obscure, somewhat more
iarai. As this chapter, though one liberty has been taken in departing
of the most important in the trea- from the letter of the original than
tise, as asserting the Logical Hypo- elsewhere.
thesis, the existence of first truths, is ' The first proof appears to be
also one ofthe most carelessly written Dialectical, because it applies to
LIMIT OF ANALYSIS. 77
proof that the series of essential predicates (which demonstrative
science alone regards) must terminate in both directions, is as
follows : — A predicate is essential if it enters into the definition
of the suhject, as divided into the definition of number : or if
the subject enters into the definition of the predicate, as num-
ber into the definition of odd.
§ 8. A succession of this latter kind of predicates must be
finite : for if there be a further predicate of odd, into whose
definition odd enters, number will be the primary subject in
the definition of that further predicate, and a limit of its de-
scending series. The terms of the ascending series must be
finite, for the whole nexus of properties must inhere in the
original subject, and the whole nexus of subjects, which is of
'equal length, must enter the definition of the ultimate property :
and as no predicate can have an infinite line of such subjects,
nor any subject an infinite line of such predicates, the ascend-
ing series must also eventually terminate.
§ 9. A succession of the former kind of predicates, found in
the d finition of the subject, must be finite : else the subject
would be indefinable : so that here too the ascending, and con-
sequently the descending, series is finite.
§ 10. If so, two extremes can only have a finite number of
intermediates,^ and demonstration has an absolute basis and
contingent predicates, as well as to belongs to Analytical Science, or
essential or necessary, and it leaves Logic,) because it rests on appro-
us in doubt whether the second kind priate principles, the definition of
of essential predicates, whose defi- essential propositions,
nition includes their subject, may It is, however, not so much a
not extend in a lateral direction proof, as a more accurate deteiTQi-
without limit ; so that the proof is nation of the principle that must be
both too extensive and too narrow. postulated. This postulate, the ex-
The second proof is merely Hypo- istence of first principles, as concern-
thetical ; there must be first truths ing the constitution of the world,
if there is science. This is a petitio appears to belong properly to Meta-
principii; for the object of proving physics, and is merely borrowed by
the existence of first truths is to Logic— See Metaph. ii. 2, and In-
prove the possibility of science ; tlfew^jjjj^ij^^
latter, therefore, must not be as- ' "CoinpS^'«iJ?OTivative laws are
sumed as a proof of the former. such as are dedu«bl|!teom, and may
The third proof is Analytical, that be resolved into, other%id more ge-
is Scientific, (for the present treatise neral ones. Ultimate ]a\t;s are those
78 ULTIMATE LAWS.
point of departure ; and they were mistaken who, we said,
denied the existence of indemonstrable truths. If demonstra-
tion has an absolute point of departure, all truths are not de-
monstrable, and the chain of deduction is not endless : other-
wise there would be no atomic and irreducible law, but every
law would be capable of resolution. Deduction does not add a
term, but interpose it between the extremes : and if deduction
were endless, two extremes would be sundered by an infinite
number of intermediates ; which, as we have shown by both
dialectical and logical proof, cannot be, as both the ascend-
ing and descending series of predication are determinate and
bounded.
CHAPTER XXIII.
ULTIMATE LAWS.
§ 1. It follows, that if two terms, neither of which is univer-
sally predicable of the other, possess the same predicate, they
need not possess it in virtue of a common intermediate. The
isosceles and scalene triangles both contain angles equal to two
right angles, and in virtue of a common character : but the case
is not always similar. If a predicate A is connected with the
subjects C and D bj' the intermediation of B, B will require
another intermediate, and this another ; and the terms sepa-
rating the extremes will be infinite. This we have shown can-
not be ; and we need not always look for a common link to
connect a predicate with several subjects, if we recognize the
existence of immediate laws. If, however, the predicate is es-
sential, the subjects must be homogeneous, and comprise the
same individuals ; for we have seen that one and the same de-
monstrative attribute cannot attach to the matters of heteroge-
neous sciences.
§ 2. If the proposition, B is A, has an intermediate, it is de-
monstrable ; and the elements of its deduction will equal in
which cannot. We are not sure that resolution of a derivative law into
any of the uniformities which we more general laws, brings us nearer
are yet acquainted with are ultimate to them." — Mill, System of Logic,
laws; but we know that there must lii. 14.
be ultimate laws, and that every
ULTIMATE LAWS.
79
number the intermediates, being composed of the immediate
laws, or such of them as are universal. Immediate and pri-
mary laws are incapable of deduction, and require a diiFerent
method of discovery.* The deduction of negative theorems also
depends on the existence of antecedent negations : and the an-
tecedent intermediate laws compose the elementary principles
of their deduction ; so that primary and indemonstrable truths
win be negative as well as affirmative.
§ 3. We demonstrate that A attaches to B, by showing that
A attaches to C, and C to B : and thus we never introduce a
class higher than A; but continually condense the middle
■ terms,2 till the theorem is resolved into its indivisible laws, or
the units of truth.* An unit of truth is an immediate law, for
such is absolutely One.
' The inductive method.
^ KaTairvKvovrai Kai av^CTat 'i<oe
av UQTa ajivsa i\Sy. — Chap. 14.
' TO kvl clvai TO iikrptf dvai irpii-
Tif tKaaTov yivovg . . (cat Xkyerai jii-
rpoVj 1^ iTpwTt^ €Kat7T0v ytvwffKsrai'
. . iv Trafft S^ tovtoiq iikrpov Kai
dpxv '^^ " fai aSiaipirov' iinl Kai
kv rate ypaniiale xpfivrai log dro/ty
ry TToSiaig, . . , aei Si avyysvkg ri fii~
rpov' iuyt9Sjv pXv yap fisyeOog, Kai
Kaff iKaaTov, jiiiKOVQ ftrJKOQ, irXd-
Tovg wKdrog, tpiavSv ijxovV) Pdpovg
Pdpog, fiovdSiav jiovoQ. — Met. x. 1.
^ yap •jrpiitrqt yviopi^ojisv rouro
irpSiTov fiETpov iKaarov ykvovg. ap-
XV oiv Tov yvbtpiffTov Trepl sKaffrov
ykvoQ 7-6 %v. — Met. v. 6.
Kai iv iravTi kari n Urcpov viroKii-
fuvov oXov iv apjioviq, SiiaiQ, iv Sk
fiEykOu d&KTvXos fi irois, iv Si pv9-
/loig pdne ^ er«XXa/3^, Kai iv fidpu
aTaOfioQ Tig i>piafi,kvag. — Metaph.
xiv. 1.
Measure was the word used by the
older Greeks for what was afterwards
called the Criterion. The final Cri-
terion or Measure of truth, accord-
ing to Aristotle, are the immediate
propositions, the elementary percep-
tions of reason. The Measure of
truth may be illustrated by compa-
rison with analogous Measures.
It must be homogeneous to the
objects measured : the measuring
unit of dimension, weight, sound,
colour, will be a dimension, weight,
sound, or colour; and as objects
measured differ in kind, so will the
measuring units. In like manner
the measuring units of science, the
first principles, must be homoge-
neous to the conclusions, (Post.
Anal, book i. 7, 9, 27, 32,) and wiU
vary in different sciences. This was
urged against the Platonists, who
overrated the universality of first
principles.
The knowledge of the object mea-
sured, length for instance, is indi-
rect, by calculation, or reference to
the standard unit of length: the
knowledge of the unit is direct ap-
prehension by Sense or Imagination.
So the knowledge of scientific con-
clusions differs from the knowledge
80 ULTIMATE LAWS.
The beginning or basis of a system is simple and uncombined,
and varies in different systems : in a system of weights the unit
is a mina ; in musical sounds the unit is a semitone ; in demon-
stration the unit is an immediate law : in science and deductive
thought the unit is reason.
Affirmative deduction, as we said, assumes no class higher
than the predicate.
§ 4. A negative syllogism in the first figure assumes no term
higher than the predicate. The conclusion, no B is A, is proved
by the premisses,
no C is A
all B is C:
and this major premiss, no C is A, by the antecedent premisses,
no D is A
all C is D:
so that we never introduce a class higher than A.
§ 5. In the second figure we prove the conclusion, no E is D,
by the premisses,
all D is C
no E is C:
or the conclusion, some E is not D, by the premisses,
all D is C
some E is not C :
so that the classes we introduce, though higher than D the
major, are not higher than E the minor.'
§ 6. In the third figure we prove that some C is not A, by
the premisses,
some B is not A
all B is C:
so that the middle introduced is lower both than minor and
than major.
of principles : the former is Infer- Deductive Science,
ence, the latter Reason or imme- ' The syllogisms examined are in
diate intuition. The existence of Camestres and Baroko : in Cesare
these measuring units in the mind and Festlno the middle term is
and in nature is the hypothesis to higher than the minor, but not
which we are driven by the idea of higher than the major.
[81 ]
CHAPTER XXIV.
COMPARISON OF PABTICULAK AND COMMENSURATE PROOF.
§ 1. Proofs are commensurate or particular, affirmative or
negative, direct or indirect ; and their comparative merits are
disputed. Let us compare first commensurate and particular.
§ 2. Particular proof may seem to be preferable as conveying
greater knowledge : for knowledge is the end and aim of proof;
and our knowledge of a subject is greater when we know its
attributes as essential, than when we know them as accidental.
Our knowledge of the musician Coriscus is greater when we
know that Coriscus is a musician, than when we know that a
man is a musician. Commensurate proof connects the attribute
essentially with a second subject, with the original only acci-
dentally : it does not attach the attribute of containing angles
equal to two right angles to the essence of isosceles, but repre-
sents it as accidental. If essential proof deserves the prefer-
ence ; as particular proof connects the subject essentially with
the predicate, particular proof is preferable.
§ 3. Secondly, whereas commensurate proof treats of unreali-
ties, and inspires us with an opinion of their reality ; leading us
to believe in the existence of a triangle, figure, and number,
distinct from individual triangles, figures, and numbers ; and in
the definition of proportional, asserting that it transcends and
is distinct from number, line, surface, and solid ; particular
probf, being neither about unrealities nor delusory, is preferable
to commensurate.
§ 4. It may be answered, that the first consideration is rather
in favour of commensurate proof than of particular. If we
prove of isosceles an attribute essential to triangle, the predicate
is accidental. If the attribute of containing angles equal to
two right angles is demonstrable of triangle, it is essential to
triangle and accidental to isosceles. If triangle is a higher
class, and univocal, and universally possessed of the attribute,
it, and not isosceles, is essentially connected with the attribute.
M
82 PARTICULAR PROOF.
Commensurate proof, then, as engaged with essential predicates,
is preferable to particular.
§ 5. If the commensurate is univocal, it has more of reality
than some particulars, they being perishable, while it is im-
perishable : and its unity does not compel us to believe its se-
parate existence, any more than the separate existence of quality
or quantity, or action or passion. If we believe it, we are to
blame, and not the commensurate.
§ 6. A demonstration is a proof exhibiting the attribute's
cause and reason : the cause is only exhibited by commensurate
proof: for the commensurate subject is primary, and the pri-
mary is essential, and the essence of the essential subject is the
attribute's cause. Commensurate proof, therefore, is preferable,
as exhibiting the attribute's cause and reason.
§ 7. Our inquiry into the cause of a change or state does not
cease, and we do not consider it known, till no ulterior cause is
assignable : the explanation is not finished and complete till it
proceeds from the ultimate cause. What was A's motive in his
departure ? The receipt of money. What was his motive in
this ? The payment of his debt. What was his motive in this ?
The performance of his duty to his neighbour. When no ulte-
rior motive is assignable, the last motive is called the final cause
of a state or change ;' and when we know this, we know the
reason of an action. This is no peculiarity of the final cause :
' An instance of reasoning from vvapxti Sk rodl Swafief tovto £k
the final cause, such as takes place ■^Sr/ sir' aiiTif.
in art and practical deliberation, is Compare : ol yap avWoyuTfioi tSiv
given, Metaph. vii. 7. rrpaKTui vapxfiv exovTie daiv, iTniSii
d-nb TkxvriQ Si ylyvtrai S>v ri ilSog roiovSe to rsKoe, &c. — Nic. Eth. vi.l2.
ev ry ^vxy. yivtrai ycip rb vyikg Resolve, as well as Science, implies
voriaavTog, lireid^ roSc vyUia, 6,vay- a. conception of ultimate reasons, oi/c
Kjj, ei vyiig iarai, Toll iirdp^ai, oiov inn iravriiiQ ixovTog ivOpdvov rj
o/iaKoTiira- it Si tovto, BtpfioTnira- irpoaipemg, ovSi yccp ^ovXtiaaadcu
Kal ovTiog ad voti, eug av dyayy dg oiS" viroXri^ig row SutTi. tan yap
TOVTO b aiiTbg Svyarai icxarov ttoi- fiovXivriKbv Trjg ipvxrjg rA BtioptjTi-
"v. Kbv airiag nvog- Tb yap ov 'ivcKa
And again : d vyiavOriaeTai Sit fiia tSiv aiTiiov kari . . . Sib olg /iri-
oiia\vv9rjvai- t'i ovv Ioti to bfiaXw- 9dg kutui axoirbg ov jSovXevTiKot. —
Orjvai ; ToSi' tovto S' larai d 0ep- Ethic. Eudem. ii. 10,
fiavOrjfTtrai. tovto Si ti Iuti, toSL'
PARTICULA-R PROOF. 83
and as our knowledge of the motive is incomplete till no ulte-
rior motive is assignable, so, in general, our knowledge of a
cause is incomplete till no ulterior intermediate can be assigned.
A given figure's exterior angles are equal to four right angles.
Why ? Because it is an isosceles. Why has an isosceles this
property ? Because it is a triangle. Why has a triangle ? Be-
cause it is a rectilinear figure. If this reason is ultimate, it
completes our knowledge. This ultimate explanation, which
alone is adequate, is commensurate.
§ 8. Objects are knowable so far as they are determinate, and
unknowable so far as they are indeterminate : now particular
objects are infinite, while commensurate are simple and deter-
minate, being the limits and determinations of the infinite. If
then knowledge is greater, the more knowable its correlative
objects, commensurate proof, as surpassing its rival in degree of
knowledge and demonstrativeness, claims our preference.
§ 9. A proof of two propositions is better than the proof of
one : commensurate proof, therefore, is better than particular :
for the commensurate conclusion includes the particular, but
the particular conclusion does not include the commensurate.
§ 10. In proportion as a proof is commensurate, the premiss
approaches to an elementary law :i when we have reached the
immediate premiss we have reached the' elementary law. De-
duction is perfect when it commences from the primary law : in
proportion, therefore, as our premisses approach the primary
law, our deduction approaches perfection. If the proposition,
' " It is of importance to remark more to be relied on ; there are
that when a sequence of pheenomena fewer chances of their being ulti-
ia thus resolved into other laws, they mately found not to be universally
are always laws more general than true .... They are more nearly un-
itself. The law that A Is followed conditional ; they are defeated by
by C is less general than either of fewer contingencies ; they are a
the laws which connect B with C nearer approach to the universal
and A with B . . . . Jfot only are the truth of nature .... There needs no
laws of more immediate sequence more to show how much more ge-
into which the law of a remote se- neral the elementary laws must be,
quence is resolved laws of greater than any of the complex laws which
generality than that law is, but (as a are derived from thera." — System of
consequence of, or rather as implied Logic, by J. S. Mill, book il. 12.
in, their greater generality) they are
84 NEGATIVE PROOF.
D is A, has the intermediates C and B ; if B is a higher class
than C, commensurate deduction will begin with B.
§ 11. Some of the above proofs are dialectical. The doctrine
is clear, if we consider that a man who knows the commensu-
rate virtually knows the particular. He who knows that every
triangle contains angles equal to two right angles, though igno-
rant that the isosceles is a triangle, virtually knows the predi-
cate of the isosceles. But if he knows the particular conclu-
sion, he neither actually nor virtually knows the commensurate.
Again, the particular is an object of sense, the commen-
surate of reason.
CHAPTER XXV.
COMPARISON OF AFFIRMATIVE AND NEGATIVE PROOF.
§ 1. We have shown that commensurate proof is better than
particular : we proceed to show that affirmative is better than
negative. Assume that proof from fewer petitions, hypotheses,
or propositions, is, ceteris paribus, preferable to a longer deduc-
tion : for if the conclusion conveyed is equally certain, the
shorter proof conveys it with greater rapidity. To prove com-
mensurately the proposition, that preference should be given to
the shorter proof, suppose that the certainty of the premisses is
equal, and that the certainty of the conclusions varies according
to their order of sequence : and let the conclusion, E is A, be
drawn either through the middles, D, C, B, or through the
middles, G, F. The proposition, E is A, as concluded in the
second deduction, is equally certain with the proposition, D is
A, as concluded in the first deduction ; but, as concluded in the
first deduction, it is not so certain as the proposition, D is A ;
for a conclusioi) is not so certain as its ground and antecedent.
A preference, therefore, is, ceteris paribus, due to the shorter
deduction.
Though both negative and affirmative deduction assume three
terms and two premisses, yet, as the former only asserts exist-
ence, the latter both existence and non-existence, the latter
NEGATIVE PROOF. 85
requires more propositions, and is therefore inferior to the
former.!
§ 2. Again, we know that one premiss must always be affirm-
ative, as two negatives produce no conclusion : hence, in de-
ducing the premisses from their ultimate laws, the affirmative
propositions increase with greater rapidity. If you wish to
demonstrate the premisses,
no B is A
all C is B,
interpose the middles D and E : the proposition, no B is A,
will follow from the premisses,
no D is A
all B is D;
and the proposition, all C is B, will foUow from the premisses,
all E is B
all C is E:
thus the deduction has added one negative and three affirmative
premisses. And so in any further prosyUogisms ; every affirm-
ative conclusion deriving from two affirmatives, and every ne-
gative from a single negative.
If then the ground of proof is more certain and credible than
the conclusion ; and the affirmative is employed as ground of
the negative, but the negative not as ground of the affirmative ;
the latter, as antecedent and more evident, claims a preference.
§ 3. The element of deduction is a commensurate immediate
proposition, and is affirmative or negative according to the con-
clusion. As existence precedes non-existence, so the affirma-
tive precedes and explains the negative. Affirmative proof,
therefore, as composed of preferable elements, is preferable to
negative proof.
§ 4. As implied in the existence of negative proof, and not
implying it reciprocally, affirmative proof has a more primordial
and elementary character.
' The commentators observe that premisses has nothing to do with
this is a fallacy, as the number of their quality.
[86 ]
CHAPTER XXVI.
COMPARISON OF DIRECT AND INDIRECT PROOF.
§ 1. Having shown that affirmative proof is better than ne-
gative, we proceed to show that direct is better than indirect :
and first let us examine their difference.
The premisses,
no B is A
all C is B,
furnish a direct proof of the proposition, no C is A. Indirect
proof assumes the contradictory of the proposition it wishes to
establish, and educes a confessedly false conclusion. If we
wish to establish that some B is not A, we assume the pre-
misses,
all B is A
all C is B:
from these results the confessedly false conclusion, all C is A ;
and as the minor premiss is unquestioned, the major must be
false, and therefore some B is not A. The position of the
terms in the two syllogisms is similar ; but there is a difference
in the evidence of the propositions. In the former the propo-
sition, no B is A, is more evident than the proposition, no C is
A, and is employed in its direct proof: in the latter the propo-
sition, some C is not A, is better known than the proposition,
some B is not A, and is employed in its indirect proof.
§ 2. The proposition, no B is A, which constitutes the evidence
in the direct proof, is naturally and absolutely antecedent to the
proposition, some C is not A, which gives evidence in the indi-
rect proof; the former being ground, the latter conclusion.
The conclusion of indirect proof, some B is not A, is not a
proper conclusion,^ and its evidence, some C is not A, is not
the proper ground ; the subject of the latter proposition, C, not
' The ultimate conclusion of an and the premisses (ekeTvo) are not
indirect proof (ft avfi^aivci ivaipn- naturally premisses (i? uv) : for the
aOm Ti) is not naturally a conclusion ; former, some B is not A, is the sub-
COMPARATIVE PERFECTION OF SCIENCES. 87
being related to the subject of the former, B, as a whole to a
part ; which relation constitutes the ground and conclusion of a
syllogism. As, then, direct proof employs absolutely antece-
dent and clearer premisses, it is preferable to indirect, even
when its conclusion is negative ; much more so when it is affirm-
ative.
CHAPTER XXVII.
COMPARATIVE rtlRFECTION OF SCIENCES.
§ 1. A science which exhibits the reason of a fact is exacter
and holds a higher rank than a science which exhibits the fact
alone.
§ 2. The science of an abstract and insulated subject is ex-
acter than a concrete science : as Arithmetic is exacter than
Harmonics.
§ 3. The science of a more elementary subject is exacter
than that which treats of several elements combined ; as Arith-
metic than Geometry. There is a combination and complexity
of elements in the subject of the one compared with the subject
of the other : for points are placed, and units are placeless.
CHAPTER XXVIII.
UNITY OF SCIENCE..
§ 1 . It is generically one and the same science which treats
of the whole of a genus, including the specific derivatives from
its elements, and their parts and essential attributes. i Sciences
altern of one of the premisses of de- ' iraaai ai iiriaTfijiai vipi tv ri'
moastrative proof; and one of the Koi yivog ri Trepiypa^dfuvai . . ovtu
latter, some C is not A, is the subal- ret Kaff avrA, virap%ovTa r<^ yivu
tern of the conclusion of demon- ■Kipi o daiv awodeucvvovin. — Met. vl.
strative proof. rl> l| oJ avWoyiv- 1. at iirutrfinai piipoc n tov ojtoe
fwe, means, a natural premiss. inonnvofuvai Biiapovai Trepi tovto
88 UNITY OF SCIENCE.
have not this generic identity, if neither the elements of the
one are derived from the elements of the other, nor the ele-
ments of both from the elements of the same third science.
§ 2. This must be tested by examining the indemonstrable
propositions on which they ultimately rest; for the principles
should be homogeneous to the conclusions : and this again may
be tested by examining whether the conclusions are homoge-
neous to one another.
CHAPTER XXIX.
SEVERAL PROOFS OF THE SAME CONCLUSION.
The same attribute is susceptible of several demonstrations,
not merely by a remoter term of the same series, but by a term
taken from a heterogeneous series. Pleasure may be proved to
be change because it is excitement, or because it is supervening
calm : which intermediates belong to different categories. They
must, however, be mutually attributable,* as both are attributes
of the same subject. We ought to examine under what condi-
tions the other figures enable us to prove the same predicate by
different intermediates.
CHAPTER XXX.
CHANCE.
The effect of chance cannot be a conclusion of [demonstrative
science, for .it is what remains when we exclude the necessary
or general. The premisses of deduction are always either ne-
cessary or general, and give respectively a necessary or general
t6 ffu/*,8E/3)jKoe. — Met. iv. 1. liirav- iariv imaTr)fi7]Q rif yivu, to. re iXSti
roe ^^ ylvoDg Kai aiaOtiinc jiia ivbg rS)v eiSSv. — Met. iv. 2.
Kai eTrurTrtjirf olov ypap-fiariRri jiia i There will be a syllogism in
ovaa irdaas Biiopii T&t ^o)vag. Sw Darapti. (B. St. Hilaire.)
Kai rov ovtoq ^<Ta e"tSfj 9iUip7}ffai fiiUQ
SENSATION. 89
conclusion : the result, therefore, of chance, being neither ne-
cessary nor general, cannot form a demonstrative conclusion.
CHAPTER XXXI.
SENSATION.
§ 1. Sensation is not science. Though the correlative of
sense is generic, the correlative of sensation is particular, deter-
minate in time and place, and incommensurate : the demonstra-
ble is commensurate : sense perception, therefore, is unscien-
tific. If we could see with our eyes that the angles of a triangle
are equal to two right angles, we should not, as some assert,
already have scientific knowledge, but should want demonstra-
tion. A spectator on the moon, who saw the earth intervening,
would not know the cause and commensurate reason of eclipse.
Repeated sensations, however, disclose the commensurate, and
prepare the way for demonstration.
§ 2. The value of the commensurate view arises from its in-
dicating the reason. It is preferable, therefore, to sensation
and intellectual intuition only when an effect is separate from
its cause, not when an object is elementary.^
§ 3. Sense, then, is not the science of the derivative and de-
monstrable; unless we use the word sense to mean scientific
demonstration. It would sometimes, however, put an end to
inquiry; not as conferring knowledge, but as leading to a com-
mensurate view. If we saw light permeating the pores of glass,
we should know the cause of transparence, sense perceiving
the particular, and reason the universal.
' It is worth observing that intellectual intuition is here opposed to
universal or abstract conception <
[90]
CHAPTER XXXII.'
MULTIPLICITY OF SCIENTIFIC PRINCIPLES.
§ 1. The principles of all deduction are not identical, as may
be shawn by dialectical considerations.
' This chapter is closely con-
nected with chaps. VII. IX. xxTiii.
The chief point in which Plato's
Logic differed from Aristotle's seems
to have been the closer connection
which he made between the Primary
and Secondary sciences. He seems
to have thought that the ultimate
premisses of the secondary sciences
are deducible from propositions of
some primary science. This is op-
posed to the rule of Appropriate
principles, which guards the variety
and multiplicity of the body of truth,
that is endangered by the exclusive
desire of unity, (oi /i^ Jk tS>v oi-
Kt'uov apx^v \6yoi Ktvoi' Ik Si rdv
turapx""'"'"'' ''V y^"" ^tiiip&v av
Tig ftaXkov \a.j3oi Tr)v airiav. De
Gen. An. ii. 8.) This precept is the
assertion of the inductive against
the deductive tendency, and always
requires to be re-enforced when a
new department of nature is to be
explored, as the first explanations
are generally vain attempts to apply
old laws to the solution of new phae-
nomena. See Philosophy of the In-
ductive Sciences, book ii. 3. Com-
pare Cicero: Omnia hsec, quae su-
pra et subter, unum esse, et un^ vi
atque un^ consensione naturae con-
stricta esse dixerunt. Nullum est
enim genus rerum, quod aut avul-
sum a cseteris per seipsum constare.
aut quo caetera si careant, vim suam
atque seternitatem conservare pos-
sint. Est enim ilia Platonis vera
vox, omnem doctrinam harum in-
genuarum et humanarum artium
uno quodam societatis vinculo con-
tineri. — De Orat. iii. 6.
The question is proposed by Mr.
Mill : " Since we are continually
discovering that uniformities, not
previously known to be other than
ultimate, are derivative, and re-
solvable into more general laws;
since (in other words) we are con-
tinually discovering an explanation
of some sequence, which was pre-
viously known only as fact; it be-
comes an interesting question, whe-
ther there are any necessary limits
to this philosophical operation, or
whether it may proceed until all the
uniform sequences in nature are re-
solved into some one universal law.
For this seems, at first sight, to be
the ultimatum towards which the
progress of induction, by the De-
ductive method, resting on a basis
of observation and experiment, is
progressively tending." — System of
Logic, iii. 14. He decides " that
the ultimate laws of nature cannot
possibly be less numerous than the
distinguishable sensations or other
feelings of our nature."
MULTIPLICITY OF SCIENTIFIC PRINCIPLES. 91
Firstly, they differ like the conclusions in truth and false-
hood : for though a true conclusion may result from false pre-
misses;' this is the only case in which premiss and conclusion
differ in character. The true conclusion, C is A, may result
from false premisses, C is B, B is A : but if the latter are de-
duced, the premisses of their deduction must be false ; for false
conclusions can only derive from false premisses, as true pre-
misses involve a true conclusion. Secondly, false principles
differ among themselves, for they are inconsistent and contrary.
§ 2. The same may be evinced by an appropriate deduction.
The elementary conceptions of many departments of nature are
heterogeneous, and inapplicable beyond the limits of their ap-
propriate science. The theory of points, which are placed, can-
not introduce into its syllogisms the conception of units, which
are placeless. The transferred conceptions would have to ap-
pear as predicates of the major term of the science to which they
were transferred, or as subjects of the minor, or as interme-
diates to major and minor : or in all positions ; some as supe-
rior to the major, others as inferior to the minor, and a re-
mainder as intermediate to major and minor : but they cannot
occupy any of these places.
There are no common principles from which all truth can be
deduced ; such as the canon, that either aifirmative or negative
must be true.^ For subjects are heterogeneous ; and some pre-
dicates are peculiar to the genus of magnitude, others to the
genus of quality ; and subject and predicate must be both
defined, and then conjoined by the general canon.
§ 3. Besides, the number of principles nearly equals the
number of conclusions: and for every new conclusion a new
proposition introduces a new conception, whether inferior to
the minor, intermediate, or superior to the major.
§ 4. Again, as conclusions are infinite, and each succession of
(homogeneous) terms is finite, (there must be an infinite variety
of heterogeneous successions.^)
§ 5. -Again, some principles are contingent, others necessary.
§ 6. It is plain that, if conclusions are infinite, principles can-
not be identical, as we have interpreted the expression. If it
' See Locke, as quoted in Appendix A. ' See chap. xxii.
92 MULTIPLICITY OF SCIENTIFIC PRINCIPLES.
is only meant that there are principles of Geometry, principles
of Arithmetic, principles of Medicine, and principles of every
science, it is absurd to call them identical because they are what
they are, for thus every thing is identical.
§ 7. It cannot be meant that every premiss will prove every
conclusion ; for this is at once refuted by Logical theory, or by
inspection of existing sciences : for principles are immediate
propositions, and a fresh conclusion cannot be obtained without
a fresh immediate proposition. If only primary immediate pro-
positions are allowed to be principles, there is one peculiar pri-
mary proposition to every heterogeneous matter.*
§ 8. If it is neither asserted that any premiss will prove any
conclusion, nor allowed that the premisses of each science are
peculiar ; it may be maintained that all principles are specifi-
cally diverse, but identical in genus. This cannot be, for we
have seen that the primary laws of heterogeneous matters are
themselves heterogeneous. There are two classes of primary
laws : the canons are common to all sciences ; the subject, as
number, or magnitude, is the exclusive domain of a particular
science.
' " For example ; since there is a tiny of the phsenomena, whatever
phsBuomenon sui generis called co- number of hidden links we might
lour, which our consciousness testi- detect in the chain of causation ter-
fies to be not a particular degree of minating in the colour, the last link
some other phsenomenon, as heat, or would still be a law of colour, not a
odour, or motion, but intrinsically law of motion, nor of any other
unlike all others, it follows that phaenomenon whatever .... White
there are ultimate laws of colour; colour can in no manner be ex-
that though the facts of colour may plained exclusively by the laws of
admit of explanation, they never can the production of red colour. In
be explained from laws of heat or any attempt to explain it, we cannot
odour alone, or of motion alone, but but introduce, as one element of the
that, however far the explanation explanation, the proposition, that
may be carried, there will always some antecedent or other produces
remain in it a law of colour . . . and the sensation of white." — Mill, Sys-
however diligent might be our scru- tem of Logic, iii. 14.
[93]
CHAPTER XXXIII.
SCIENCE AND OPINION.
§ 1. Knowledge or Science and its object differ from Opinion
and its object.
Knowledge is commensurate, and rests on necessary grounds.
Contingent truths cannot be objects of knowledge, else they
would both be necessary and non-necessary : nor can they be
objects of Reason, for Beason is the beginner of Science ; nor
of indemonstrative science, for this is the apprehension of im-
mediate propositions -A and as all apprehension of truth is either
Heason, Science, or Opinion, it follows that Contingent truths
are the object of Opinion. This is confirmed by phsenomena :
the truth of Opinion is precarious : this is explained, if its object
is the mutable. When a man regards a fact as necessary, he
regards himself as possessed of Knowledge, not of Opinion :
when he regards it as actual but contingent, he regards himself
' as possessed of Opinion, not of Knowledge : confirming our
position, that the contingent is the object of Opinion, the ne-
cessary of Knowledge.
§ 2. Can the same thing in any sense be an object of both
Opinion and Knowledge, and can we, without identification of
Opinion and Knowledge, maintain that every object of Know-
ledge may be an object of Opinion ? For then Opinion might
follow the steps of Knowledge along the intermediates till it
arrives at the immediate, and why should the one be Knowledge
and not the other ? For the reason or intermediate kw, as well
' Beason, Science, and Opinion, Itrurriiiiri, Kai So^a, Kai ^pSvting
are three species of intellectual ap- (vove). — De AnimS,, iii. 3.
prehension : Reason apprehends first Swdfuie Kaff dg Kpivo/iEv, alaBi]-
principles, Science necessary conclu- atg, So^a, vovg, iirurrijiiti. — Ibid,
sions. Opinion contingent proposi- rb voiiv (Ji'noKaji^avuv) (ppovtimg,
tioii5_ (voSj) Kai iiriBTrinr), Kai WJa. — Ibid.
tiai Si Trje viroXffij/eiag Sia^opai,
94 SCIENCE AND OPINION.
as the fact, may be the object of Opinion. Apprehension of a
necessary conclusion, based on the definitions which form the
legitimate grounds of demonstration, is Knowledge, not Opi-
nion. Apprehension of a proposition as true, but not as educi-
ble from essential and definitive theorems, is Opinion, not
Knowledge.! if based on immediate propositions, it is Opinion
both of fact and of reason : if not based on immediate proposi-
tions, it is Opinion of fact alone.
§ 3. The object, then, of Science and Opinion is only iden-
tical in a manner similar to that in which the object of true and
false apprehension is identical. If the object of true and false
Opinion were identical in the way in which some explain,
among other strange results it would follow, that a false Opinion
is no Opinion. But the word Identical is equivocal : the object
of true and false Opinion is identical in one sense, and not in
another. The commensurateness of diameter and circumfer-
ence, which is an object of false belief, is not in the same man-
ner an object of true belief. While the material element, the
terms of the theorem, is the same, the formal elements are op-
posed : so that the object of true and false belief must be partly
identified and partly distinguished. The same holds with
respect to the objects of Science and Opinion. They agree in
the subject and predicate of their theorem, and agree in their
conjunction, but difier in the mode of their conjunction ; the
one connecting them necessarily and essentially, the other con-
tingently and accidentally.
§ 4. It follows, that Knowledge and Opinion of the same fact
cannot coexist in the same mind: for we cannot believe one
and the same truth to be both contingent and necessary.'^ The
object of Opinion and Knowledge may be identical in two dif-
ferent minds, but not in the same mind : for we cannot at the
same time entertain the two beliefs, that the conjunction of
* W7rap;^€w war ovffiav Kai Kara, rtj^ to. Ka96\ov ov x*^p^f^^ eTroUt
TO elSog. Science then rests on a oiSi roii£ bpia/jiovQ' oi S" Ixdipiaav,
knowledge of the Idea according to Kai t& roiavra tUv ovriav 'iSkag
both Plato and Aristotle. They dif- jrpoff^jyoptwtraj/. — Met. xiii. 4.
fered, however, as to the nature of ' The Axiom states that nothing
the Idea, though they would express can be the subject of contradictory
it in the same definition. 6 JiwKpd- predicates.
SAGACITY. 95
man and animal is accidental or contingent, and essential or
necessary.
§ 5. Further distinctions between Inference, Reason, Science,
Art, Wisdom, Philosophy, belong rather to Physical or Moral
Science than to the present treatise.*
CHAPTER XXXIV.
SAGACITY.
Sagacity is a talent of guessing rightly at the -intermediate
when there is no time for consideration. A man observes that
the bright side of the moon always faces the sun, and quickly
divines the explanation that her light is borrowed : or observes
a man in conversation with a capitalist, and conjectures that his
object is a loan : or understands the friendship of two persons
by referring it to a common enmity. In all these cases the
extremes are observed, and at once deduced from the interme-
diate causes. The moon, C, shines with light borrowed from
the sun, B ; and therefore, its luminous face is opposite the
sun, A. The conclusion, C is A, is noticed, and immediately
analysed into its premisses, C is B, B is A.
' Psychology, or at least a per- ^vxr) Kivrjaeiog dpx4 ovSk ra /jiopia
tion of it, belongs to Physical sci- Siravra . . . SrjXov ovv i>£ ov Trepi
ence. \sktcOV av eiij ti^ 'jrtpi ^iktsuq 'Trdtnjg ^XVQ \eKTeov. oiiSs yap wa-
9iii>pr)nKff TTipl \l/vx^£ liaXKov rf Trig aa ifa)x>) ipvaig, aXKd ti fwpiov airrje
vXris, '6a(f fidWov 17 iiXij Si iKeivrjv iv rj Kai TrXeiu). — De Part. Anim. i.
j>vaig lar'tv ri dvairaXiv . . . diropj]- 1. Kal ircpi ^x^S iviag Btbiprjirai
ff£i£ S" av Tig jrSTCpov irepl irdarig rov (jniaiKov, o(ra nf) dvev rrjg ii\)jg
^vxvg Trjg (pvaiKrig lore rb tiireiv, f) kariv. — Met, vi. 1 ; Nic. Ethic, vii. 3.
TTepi Tivog . . . ^ ovK effTi 'ffdira iy
BOOK II.
CHAPTER I.
PROBLEMS OF SCIENCE.
§ 1 . Problems and theorems are equal in number : problems
are four :
(1) The question of Fact : Has a given subject a certain
attribute ?
(2) The question of Keason : What is the cause that a given
subject has a certain attribute ?
(3) The question of Existence : Does a given subject exist ?
(4) The question of Essence : What is the nature of a given
subject ? 1
§ 2. The ■word,'^ Whether, when we inquire Whether this or
that of certain enumerated cases is true, as when we inquire,
Whether or not the sun is eclipsed, generally indicates a ques-
tion of Fact : for the inquiry ceases when the Fact is known ;
and, if known at first, the word Whether does not enter the
question.
§ 3. The inquiry into the Reason follows upon knowledge of
the Fact : when we know that the earth is subject to earth-
quakes, and the sun to eclipse, we inquire, what is the cause of
earthquake and eclipse ?
§ 4. It is a different problem, when we inquire into the ex-
istence or non-existence of an agency or substance : as when
we ask. Is there, or is there not, a centaur ? Is there, or is
there not, a God ?
' The two last of these are pro- i. 10), so that, to a certain degree,
blems of Inductive, but first princi- the second problem also is assumed
pies of Deductive Science ; the one among the principles of Demonstra-
being the hypothesis, the other the tion.
definition. The attribute, as well as ' kv rotj avTucu/dvoig dtl roO to-
the subject, must be defined (bopk rkpov ij Kfirtjaig. — Met. x. 5.
A MIDDLE TERM THE OBJECT OF INQUIRY. 97
§ 5. When we know the Fact that an agency or substance
exists, we inquire into its Essence or nature : What is the na-
ture of man ? What is the nature of a God ?
CHAPTER II.
THE OBJECT OF INQUIRY IS ALWAYS THE INTERMEDIATE.
§ 1. Problems and theorems may be classed as above. When
we inquire (1) the Fact, whether a subject possesses an attri-
bute ; or (3) the simple Existence of the subject ; our inquiry
is. Has it, or has it not, an Intermediate ?
§ 2. When we know (3) the Existence of a subject, or (1)
the Fact that it possesses an attribute ; in other words, when
we know the simple or modified Existence of the subject; and
proceed to inquire (4) into the Essence of the subject, or (2)
the Reason of its attribute ; then our inquiry becomes, What is
the determinate Intermediate F
§ 3. The questions (1), Does the moon wax or wane? Is the
moon eclipsed ? referring to a particular property of the moon,
are questions of modified Existence : (3), the Existence of the
moon or of night, if discussed would be a problem of simple
Existence.
Two of the problems inquire. Is there an Intermediate ? and
two, WTiat is the Intermediate ? for the object of inquiry is al-
ways a Cause, and the Cause enters as an Intermediate. To
inquire. Is the moon eclipsed? is to inquire. Is there a Cause of
the moon's eclipse ? When this is settled we proceed to in-
quire. What is the Cause of the moon's eclipse ? The Cause of
a subject's existence, or of its possessing an attribute essential
or accidental, always enters syllogism as an intermediate. By
the simply existing subject I understand the earth, the sun,
the triangle : by their modifications or attributes, equality, in-
equality, eclipse, interposition.
§ 4. The problem of Reason may be identified with the pro-
blem of Essence. The problem and solution. What is the
88 DEFINITION INDEMONSTRABLE.
nature of eclipse ? The deprivation of the moon's light by the
earth's interposition ; are identical with the problem and solu.
tion, What is the Cause of eclipse ? The earth interposing de-
prives the moon of light. The question, What is the Essence
of harmony ? and the answer, A numerical ratio of grave and
acute, are identical with the question and answer. What is the
Reason of grave and acute harmonizing ? Their having a cer-
tain numerical ratio. The question. Is it a Fact, that grave
and acute possess the attribute of harmonizing ? becomes the
question. Have grave and acute a numerical ratio ? and after
this is settled, ensues the question. What is the reason of their
harmonizing ? or, What is their numerical ratio ?
§ 5. Sensible intermediates show that the object of search is
always the intermediate ; for sensation would render inquiry
unnecessary, by indicating the commensurate antecedent. A
spectator on the moon would not need to inquire into the Fact
or Cause of eclipse, for sense would connect the particular
eclipse with the particular interposition.; and out of this he
would elicit the commensurate conjunction.
§ 6. The knowledge of the Reason, then, is identifiable with
the knowledge of the Essence. For the Essence of the subject
is the Reason of its simple existence : and the Reason of the
attribute constitutes its Essence.
CHAPTER III.
DEFINITION AND DEMONSTRATION HAVE NOT THE
SAME PROVINCE.
§ 1. The object, then, of research is always the Interme-
diate.! Let us next examine how the Essence or fundamental
character is discovered and explained, and *hat is the nature
' Mr. Whewell asserts (Philoso- discovery of the major extreme; but
phy of the Inductive Sciences, book he does not observe that what he
ii. chap. 5.) that the discovery of calls the " second extreme" is really
the middle is not so important a the middle of an original syllogism,
step in the progress of science, as the The phtenomenon that Kepler ob-,
DEFINITION INDEMONSTRABLE. 99
and the object of definition, beginning with a preliminary dis-
cussion closely allied to what has preceded ; whether the same
object under the same aspect is both demonstrable and de-
finable.
§ 2. Some matters of deduction must be indefinable, for syl-
logism in the second and third figure is negative and particu->
lar : but definition, stating what an object is, must always be
afiSrmative and universal.
§ 3. The objects of affirmative conclusions in the first figure
cannot all be definable : for, if all knowledge of the demonstra-
ble results from demonstration, all the demonstrable must be
indefinable ; else, possessing the definition and not the proof,
we might know the demonstrable without demonstration.
§ 4. The same may be seen by induction ; there was never a
case in which an attribute, essential or unessential, was learnt
by mere definition.
§ 5. If definition is limited to the characterization of sub-
stances, attributes are indefinable.*
§ 6. We have shown that some objects of demonstration are
indefinable. To show that some objects of definition are inde-
monstrable, we may repeat one of our former arguments. Unity
of the truth implies unity of knowledge ; and to know a dedu-
cible truth is to possess its deduction : a deducible truth, there-
fore, cannot be known by definition.
§ 7. Again, definitions are the principles and foundation of
deduction : and the principles are indemonstrable : else there
woul4 be elements of the elementary, and foundations of the
foundation, in endless regression. The primary or limiting
truths, therefore, are definitions incapable of deduction.
served, the conclusion of the original plained by what forces Mara was
syllogism, was : impelled in his elliptical course, in
Mars is seen in certain positions. which the forces would be the
After many unsuccessful attempts, middle.
Kepler explamed this by assuming : ' This, however, is not true. ^ 0a-
Mars describes an ellipse about vepbv 'on i irpiirwg icoi enrXHc opia-
the sun. * /«Ae Kal r6 rt ^v ilvat tSv oiaiOiv
The elliptical motion of Mars is iariv ov firfv aXXd sai rHv dWutv
here the middle; it would be the o/ioiws iffri, ttX^v oi 7rp(i™£.— Met.
major of a syllogism, which ex- vii. 4. See Post. Anal. i. 10.
100
DEFINITION INDEMONSTRABLE.
§ 8. The objects of definition, then, and demonstration are
not always identifiable : nor are they in any case. For the
defined is the essence or fundamental character, and this is
always postulated or assumed in science, not demonstrated:'
as the mathematician assumes, not demonstrates, the nature of
Unity, or the nature of Even.
§ 9. All deduction conjoins or disjoins a subject and predi,
cate : in definition there is no subject and predicate. Animal
is not attributed to Biped, nor Biped to Animal: Plain to
Figure, nor Figure to Plain.
§ 10. Again, Essence differs from Fact : the definable is an
Essence, the demonstrable a Fact : and as Essence* and Fact
are not, like Triangle and Isosceles, related as part to whole,
they require a different mode of explanation.
§ 11. We have seen that neither the whole classes of the de-
finable and demonstrable can be identified, nor any of their
members :" and the same difference that exists between the
definable and demonstrable wUl exist between definition and
demonstration.
' In the Greek we have viroTt9i-
/itvai rb ri ean: this is an inaccu-
rate expression : 6 yd.p opicr^bg Oefftg
fj£v sffTiVf viroOecFig S" oiK iffri. —
Book i. 2.
' The indemonstrability of first
truths is expressed by Plato, when
he makes Socrates as teacher pro-
fess the obstetrical art. (dyovog ii/jii.
ao^iag . . fiaievsffQai juf o Bebg dvayKa-
Zsi, yivvav SI diriKwXvtr^v. Theajt.
§ 20.) Ideas and principles must be
the spontaneous growth of the mind ;
they cannot be imparted from with-
out ; they are not, like deductive
conclusions, implied in previous
knowledge ; they require a new per-
ceptive power, and the first genuine
perception of a great principle is, as
it were, a new birth. The only
assistance to their development that
it teacher can contribute, is the use
of the Elenchus, the rejection of un-
sound maxims and distorted views,
by deducing their false consequences,
or showing their discordance with
acknowledged truth. (Paaavil^av
TTOTtpov EiS(i}\av Kai ^evSog (iffo-
TiKTU rov vkov 71 StdvoLa, rj yovifiov
T€ Kai <iX)j0lf .— Theaet. § 20. dWd
fipt Sfi avTO Koivy crKi^iifuOa, yovi-
fiov 77 dvsfiLaXov Tvyxdvet ov. — Ibid.
§23.)
[101 ]
CHAPTER IV.
CATEGORICAL PROOF OF A DEFINITION.
Beside the considerations hitherto alleged to show that
a definition cannot be deduced, we may observe that the terms
of a syllogism in which the essence is demonstrated must be
peculiar to one another and reciprocate : if A in the conclusion
is peculiar to C, A the major must be peculiar to B the inter-
mediate, and B to C the minor. Again, in order that A in the
conclusion may be essential to C, A the major must be essential
to B the intermediate, and B to C the minor. Unless we have
a pair of essential premisses, if B is not essential to C, as well
as A to B, A in the conclusion will not be essential to C. B,
then, will be the essence of C, as well as A ; and B will be its
essence antecedently to A. If C is Man, and A its deducible
definition ; B the intermediate will be a prior definition, and
some other intermediate prior to B. The minor premiss of the
deduction will always be a petitio principii; for when we assume
that C is B, we assume the essence of C. It will be better to
suppose that there are only two premisses to the deduction,
and these, therefore, primary and immediate ; and then it will
be clear, that proof by convertible propositions always involves
a petitio principii, whether Man, the Soul, or anything else is the
subject of definition. In order to prove that the soul is the ori-
ginal cause of life, because it is a self-moving number, we must
postulate that the soul in its essence is a self-moving number.
For if A is merely the predicate of B, and B of C, it does not
follow that A is the essence of C. And if A, though essential,
is only part of the essence, as animality is part of humanity,
and not identical, or the whole essence of B, and B of C ; we
cannot conclude that A is the whole essence of C. If, on the
other hand, the premisses are of this character, then B is the
antecedent essence of C, and the demonstration is vitiated by a
petitio principii.
[ 102 ]
CHAPTER V.
ESTABLISHMENT OF DEFINITION BY DIVISION.
§ 1. Division, as we saw in the analysis of the figures, cannot
enable us to deduce a definition.^ The conclusion of the pro-
cess, like the conclusion of induction, is defective in necessity.
A conclusion must not be a matter of question or concession,
but the inevitable consequence of the premisses, unaffected by
concession or denial. In establishing a definition,' you ask
whethet Man is animate or inanimate ; and assume, not deduce,
that he is animate. Again, after dividing Animal into terrestrial
and aquatic, you do not deduce but assume that he is terrestrial.
§ 2. At the end, you do not deduce necessarily, you only as-
sume, that the combination of these elements is the essence of
Man. The number of the elements is immaterial. Though the
assumptions might warrant some conclusion, the syllogism ac-
tually drawn is inconclusive : though it might be inferred that
the combination is a predicate of Man, what necessity is there
to conclude that it is his definition ?
§ 3. Again, how can you be sure that there is no excess nor
deficiency in the elements, that none were passed over in the
division ? This fault, however, though often incurred, may
be avoided, if, without pretending to deduction, we assume
only essential predicates, and carry on a continuous and unin-
termittent division till all the elements are exhausted ; which
must be the case when we arrive at a species no further divi-
sible.
§ 4. In this process, however, as in Induction, though some
truth may become evident, it is not by syllogism. Though you
close the process by selecting and putting together the defini-
tion, you do not conclude : you are just as liable to the ques-
tion, "Why ? as if you assert the necessity of a conclusion with-
out having produced any intermediate. You assert the essence
' Prior. Anal. i. 31.
HYPOTHETICAL PROOF OF DEFINITION. 103
of Man to be, wingless, biped, footed, animal : at every stage
of tbe process I demand a proof.
§ 5. You may prove, perhaps, that every thing is mortal or
immortal, and continue the subdivision : but this array of sub-
divided branches is not a definition of Man : so that, though
proof enters the division, the definition of Man is not proved.^
CHAPTER VI.
HYPOTHETICAL PROOF OF DEFINITION, AND PROOF
BY DEFINITION OF THE OPPOSITE.
§ 1. Is Definition susceptible of an hypothetical proof, if we
assume as our major, that the reciprocating combination of es-
sential predicates is the definition ; and as our minor, that cer-
tain predicates are essential, and when combined reciprocate
with the subject ; and thus conclude that these predicates com-
pose its definition ? Here, as in the former case, the minor
premiss is a. petitio principii.
§ 2. Again, in proving we do not define Proof, for the pre-
misses are always related as whole and part : so in deducing a
definition we ought not to assume among our premisses the
definition of Definition ; but as, if our proof is disallowed, we
maintain it by defining Proof ; so, if our proof of definition is
disallowed, we may answer by defining Definition.^^ As we
draw a conclusion independently of the definition of proof, so
' Though Division is no proof of proof; and the riv is in the past
Definition, yet it is of great use in tense, because the definition was as-
the investigation of a Definition, sumed before it is employed to sup-
See chap. XII. port a conclusion. At the time of
^ TovTo yip iKciTo rjiiiv rb ri ^v its assumption we may suppose that
clvai. The past tense licctro sug- the present tense was used, as above,
gests the reason why the ijv, to where a definition professes to be
which it is equivalent in the formula proved : tovto dp' lari rA ilvai
ri i}^ elvai, is in the past tense. It Ixdvif.
signifies a definition as employed in
104 PROOF BY DEFINITION OF THE OPPOSITE.
•we ought to prove a definition independently of the definition
of Definition.!
§ 3. A hypothetical demonstration, that assumed the es-
sences of opposites to be opposite, and, as dividedness is the
essence of evil, concluded that the essence of good is undivided-
ness, would be similarly guilty of a petitio principii. The
conception introduced to prove an essence must be an essence,
but not identical with the essence to be proved ; nor, as in the
case of opposites, must they possess the same definition, and
reciprocate.
§ 4. Both the proof by division and the proof by hypothesis
are liable to the objection, that they introduce in the conclusion
a unity among the elements that did not appear in the premis-
ses.* Why is Man defined to be a terrestrial biped animal, and
not rather, a terrestrial, and a biped, and an animal ? Why do
these elements combine into a single essence more than the
predicates Ghrammatical and Musical ?
CHAPTER VII.
ESSENCE CANNOT BE PROVED.
§ 1. How does Definition unfold the essence, if it neither,
like syllogism, shows that from certain assumed existences the
existence of something else necessarily follows ; nor, like induc-
tion, that a law holds because it has no exception ? Both these
methods prove existence, not essence : what other method re-
mains? The definer, surely, does not point out the essence
with his finger as an object of sensation?
§ 2. How can the Essence possibly be exhibited ? For
knowledge of the essence necessarily involves a knowledge of
the existence. We cannot understand the essence of a nonen-
' Though the hypothetical proof useful for this purpose. See Nic.
is not demonstrative, yet it is useful Ethie. TroWaicif fiiv oiv yviopiZirai
in inyestigating a definition. See ^ ivavria 'iKiS f^T* rijs ivavriag.
chap. XII. Also proof by the defi- Book v. 1.
nition of the opposite, though little ^ See Metaph. vii. 12.
more than a petitio principii, is
DEFINITION INDEMONSTRABLE. 105
tity, such as Goatstag, though we may understand the meaning
of the name. How can one and the same method evince both
the essence and the existence ? i For essence and existence are
distinct truths ; and the object of definition is single, like the
object of demonstration.
§ 3. Again, as no truth but essence is indemonstrable, and
existence is not essence,' for existent is never a genus, it fol-
' The difference between Defini-
tion and Hypothesis is pointed out
by Mr. Mill : the latter he calls a
Postulate. " The Definition of a
thing, along with the meaning of a
name, covertly asserts a matter of
fact. This covert assertion is not a
Definition, but a Postulate. The
accompanying Postulate affirms the
real existence of things possessing
the combination of attributes set
forth in the definition ; and this, if
true, may he- foundation sufficient
on which to build a whole fabric of
scientific truth." In contending,
against Stewart, that Definitions are
not the original premisses of science ;
that the conclusion follows not from
the Definition, but from the tacit as-
sumption of a matter of fact; he may
seem to have the concurrence of
Aristotle, who makes much the
same assertion : (ol opoi ovk ciaiv
vTroGeuEig. . . .aXX' tv ralg ■npordat-
aiv cCi iiroBiuEig. . ..elai ydp iirofll-
ff£Lg offiiiv ovTtav Ti^ sKetva elvai yi-
verai rh avfimpaaiia.) — Post. Anal,
i. 10. Speaking too of premisses he
onlynames the hypotheses: {aidp%al
Kai cu. Xeyofuvai vTroBeaeig avrai
liai. Post. Anal. i. 19. See also
Prior. Anal. ii. 17, and Nic. Eth. vii.
8. dpxh, uaircp iv roie /mOriiMTi-
Koig ai iiiroBiatie:) however, at other
times he only specifies the Defini-
tions, (en, aX dpxal r&v dicohi^tiiiv
opta/iot .. ..rfTa irpSira opur/ioi taov-
Tai dvavotuKTOi. — Post. Anal. ii. 3.
Kal dpxvv iiriariiiirig ilvai nva
^afjikv, y Toig 'opovg yvtttpil^Ofiev* —
Post. Anal. i. 3.) the truth being,
th^t both of these elements, as well
as the Axioms, ai'e necessary, {iviag
ft^vTOi kTTLffTrjfiag oiidkv Kio\vei tvia
TovTUiv Tcapopav . . . dW ovSiv
rjTTOv ry ye fvtrei rpia ravra iari.
Post. Anal. i. 10.) Mr. Mill indeed
says that the Postulates are the pre-
misses on which the theorems de-
pend ; and while these are retained,
it would make no difference in the
certainty of geometrical truths,
though every Definition were laid
aside ; and that the conclusions
which seem to follow from a Defi-
nition do not follow from the Defi-
nition as such, but from an implied
Postulate. (System of Logic, book
i. 8. § 6, 7.) But, like Aristotle, he
makes the Postulate include the De-
finition ; for it is the idea or object
presented by a Definition which is of
importance in demonstration, not
the name by which this idea or
object is symbolized.
' This is not accurate: only the
existence of the attribute or effect is
demonstrated : the existence of the
primary substance or cause is as-
sumed in the Postulate or Hypo-
thesis. (Post. Anal. i. 10. ; also ii.
8. rd Afitaa Kal rag dpx^S Kai elvai
106 DEFINITION INDEMONSTRABLE.
lows, that all existence is demonstrable. This is verified by the
processes of the actual sciences : the geometer assumes the
conception of Triangle, but demonstrates its existence. What,
then, does definition unfold ? It cannot unfold the essence of
Triangle, for we cannot know the essence without knowing the
existence.
§ 4. The recognized definitions never prove existence. You
define a circle to be a line equidistant from a middle point.
What necessity is there that such an object exists ? and again,
why is such an object a circle and not bronze? Definitions
neither evince the possibility of their objects' existence, nor
that they belong to the object professedly defined, but are
always open to the question. Why ?
§ 5. As definition must unfold either the essence of a reality
or the meaning of a word, and cannot unfold the essence, is it
any sentence unfolding the signification of a word ? No : else
nonentities would be definable, for their name may have a sig-
nification : and all speech would be definitions ; for every sen-
tence might be named ; and the contents of the Iliad would be
a definition of the name. Besides, the signification of a word
can no more be evinced by demonstration or definition than the
essence of a reality.
§ 6. It is clear that demonstration and definition, and the
objects of each, are distinct : and that definition is not demon-
Kai ri iariv vnoOsffBai SeXj and cLtrvvQsTOVf Kal oiiSe r6 elvai irepi
M.eta,ph.vi.l.favEpbv'6Ti oisiaTiv airov dpBSis £X<" vpoafipevra d-
diroSu^iS obaiag oidk Tov ri kanv, ttcZv. He seems to point out the
dWd Ttg dXKog rpSvoe rrjg StiXii- distinction between peculiar and
aiw£. o/ioioig S" oiS" el tariv ri /iri common principles, i. e. between
kffTt rb ykvoQ Trcpt 3 Trpayfianvov- Tiieses and Axioms, when he makes
rat, ovSiv \kyovai, Sid ro rrjg avTrjg some of the birds in his aviary keep
clvai Siavoiag to tb ri Ian SrjXov ™ flocks separate from the rest,
iroiHv Kal H tan tovto.) while others pass from one flock to
The difference between Existence another, and fly about everywhere,
and Essence, i. e. between Hypothe- ^^ tRdary -^vxy woirjamiuv irepiare-
sis and Definition, is pointed out by p^Sivd nva wavroSairGv 6pvWuiv,
Plato, Theset. § 139, and § 147, ''"£ Z'^" Kar' dyiXag ovaag xwpij
dTreSt)(^6fit9a on rHv irpianav oix ^v dWuw, rdg Si xar 6\iyag,
e'ii] \6yog, e? iJJv rd dXKa avyxHTai, Mag St fiovag Sid iraa&v 'diry dv
SioTi avrb KaO' avrb iKaarov tir/ rixuai Trtroiikvag. — Ibid. ^131.
DEMONSTRATIVE DEFINITION. 107
strative ; and that essence can be discovered neither by demon-
stration nor by definition.
CHAPTER VIII.
TWO KINDS OF DEFINITION.
§ 1. We must now reconsider whether any of the above state-
ments are inaccurate ; and again inquire what is the nature of
definition ; and whether essence in any sense is definable or
demonstrable, or absolutely indefinable and indemonstrable.
To know the essence, as we said, is the same as to know the
reason of the existence.^ For every thing has a reason : and
this is either identical with the object or distinct ; and if dis-
tinct, either demonstrable or indemonstrable. If one cause is
demonstrable, another indemonstr-able cause must be the inter-
mediate ; and the proof is in the first figure, and the conclusion
affirmative and universal. In this mode of demonstrating the
essence, we prove one definition by another ; for the interme-
diate that proves an essence or a peculiar predicate must itself
be an essence or a peculiar predicate. Of two definitions, then,
one is proved and the other assumed : and, as we said before,
this is not a demonstration, but a dialectical proof, of the es-
sence.*
§ 2. We will now start again, and show how far demonstra-
tion is concerned with the essence.
Knowledge of a cause is either subseqpient to knowledge of
the fact or simultaneous, but never antecedent : in like manner
knowledge of the essence never can precede knowledge of ex-
istence.
§ 3. Knowledge of existence is either accidental, or implies a
partial perception of the essential character -J as when we both
know the existence of thunder, and that it is a certain noise in
the clouds : or the existence of eclipse, and that it is a certain
t Post. An. U. 2. * Post. An. ii. 4. ' Knowledge of
the existence is essential when simultaneous to knowledge of the essence.
108 DEMONSTRATIVE DEFINITION.
loss of light : or the existence of man, and that he is a cer-
tain animal : or the existence of the soul, and that it is a
certain self-moving power. Accidental knowledge of the ex-
istence is no advance towards knowing the essence. To inquire
into an object's nature, without adequately knowing that it
exists, is to inquire into a nonentity. But a knowledge of its
existence, in which the object itself is partially recognized, is a
step towards a conception of its nature : so that the two kinds
of knowledge vary together in their degree of completeness.
§ 4. Suppose that the object is partially perceived : and, in
the first case, let A represent Eclipse, C the Moon, and B the
Earth's interposition. To inquire whether C is A — whether
the moon is eclipsed — is to inquire whether C is B) — whether
she has experienced the earth's interposition ; that is, whether
she has satisfied the definition of A i^ if this can be asserted in
a minor premiss, we assert the conclusion. Or, it is to inquire,
which of the contradictory majors, A or not-A, is defined by
the existing intermediate B : whether the conditions of con-
taining angles equal to two right angles, or the conditions of
the contradictory predicate, are satisfied by the triangle. When
the premisses are immediate truths, they furnish a simultaneous
knowledge of fact and of reason.
§ 5. Otherwise they inform us of the fact alone : if our
proving intermediate is the phsenomenon, that at full moon
bodies, between which and the moon there is no intercepting
body, cast no shadow, we know the fact of eclipse without the
cause, the existence without the essence.
§ 6. When we know the fact that C is A, to inquire into its
reason, B, is to inquire into the definition of A the major : is it
the earth's interposition, or the moon's extinction, or rotation
on her axis ? Let C represent a Cloud, A Thunder, B the ex-
tinction of fire. What is the reason that a cloud thunders ?*
Because fire is extinguished in the cloud. We have the syl-
' That Xoyoe here means defini- aKpov Bib iraaai ol einirrrjiji.ai Si
tion appears from a passage below : opurjiov yivovrai.
Kal iuTi ye \6yoQ rb B roii A ro5 ^ This definition is given by
irpiiTov oLKpov : and from chap. xiv. Anaxagoras, and rejected by Ari-
ioTi Si rb fiemv \6yog row Trpiirov stotle. (Meteor, ii. 9.) His own ac-
ELEMENTARy DEFINITION.
109
logism, C is A, because C is B, and B is A : and the middle
term, B, is the definition of A the major : assuming that the
definition of Thunder is, the extinction of fii-e in a cloud. If
there is another intermediate, it will be a prior deflnition.i
§ 7. Such is the method- by which the essence is discovered :
and it appears that the definition is not demonstrable, and yet
involves a demonstration. It is true, as appeared in the pre-
liminary discussion, that essence is indemonstrable : but it is
also true, that, when an object is distinct from its cause, its
definition involves a demonstration.
§ 8. While some objects are thus distinct from their cause,
others are identical : the essence of the latter is immediate and
elementary: and both their existence and definition must be
assumed in an hypothesis, or otherwise unfolded : as the defini-
tion and existence of the monad are assumed by the arithmeti-
cian. When objects have an intermediate and a distinct cause,
their existence and essence are unfolded in demonstration,
though their essence is not directly demonstrable.
count may be given in the words of
his scholiast, (p. 269 of Ideler's edi-
tion,) yiviTui PpovT^ in T^£ Karrvui-
Sovg dva9vfitd(7su)g Iv ti^ vk^u diro'
KXeio/iivtie Kai, tov vk<povg l^wBev
irvKvovfikvov Sid Tyv ^v^iv, tKirvprj-
viZ,ofiivriQ lltaimg Kal vifr] Tiv&
7r\r\TT0variQ Kai irarayov iroiovariQ.
Compare his account of Wind : avii-
mv ij Kairvu}Sr)Q dvaQvftiaffig Kal
^kptrai irKriuiov Ttyv dTroyelov ctepogj
Kal TrpoaTTTaiovaa kvkXij) Kivov/ii-
vif aii/iari Xfirai Kai imrKavrijiivriv
lig T&. irXayia Kivitaiv iroiUTai. —
Ibid. p. 240, and of Rain : rb irtpl
Ti^v yrfv vypbv virb tGiv aKTiVbtv Kai
virb T^g dWijg rrjg avtoQsv QtpfiOTr)-
Tog dTjiiSoiiuvov ^kperai avbf Trig
Sk BepfioTiirog airoXnrovaiig rrjg dva-
yovatig aiirb, avviaraTai iraXiv ri
drftlg ^vxoftkvfj Kal ylverai ^Suipf
y£v6fi£vov Sh ^kpSTai iraXtv Trpbg rrjv
yrjv. — Meteor, i. 9. Many other
examples of causal definition may
be found in this treatise, which, like
that cited from Anaxagoras, though
false as doctrines of physical sci-
ence, may serve as models in point
of form.
' This is tlie case when the cause
is not only distinct, but also demon-
strable, {tan Ti cdrwv, Kai tovto fi
rb aiirb ri aXKo, kclv y aXKo, ^ diro-
SuKrbv r) dvairoStiKTOv. — See be-
ginning of chap.) Such a demon-
stration would be the petitio prin-
cipii discussed in chap. iv.
[ no ]
CHAPTER IX.
DIFFERENT KINDS OF DEFINITION.
§ 1 . Definition is an exposition or statement exhibiting the
essence : one kind exhibits the signification of a name, or of an
expression, such as. Triangular character, used instead of a
name. When we know that an object exists corresponding to
the name, we investigate its cause ; a difiicult investigation, be-
cause, as we said above, its very existence is hitherto unknown,
or only accidentally known.
§ 2. The Unity of a statement is constituted by aggregation :
as the Iliad is one aggregate of many statements : or by essen-
tial unity in the subject and predicate of a proposition.
§ 3. Besides nominal definition there is real definition; a
statement exhibiting the cause of existence. The former indi-
cated without proof: the latter is a demonstration of the es-
sence without a demonstrative form. When it is asked. Why
does it thunder ? the answer is, Because fire is extinguished in
a cloud. When it is asked. What is thunder ? the answer is.
The extinction of fire in a cloud. One and the same statement,
disguised in form, becomes a definition, or a proximate demon-
stration.i
§ 4. Another definition is the conclusion of an essential de-
monstration :2 as when we define Thunder, a certain noise, in
the clouds.
' i. e. a demonstration by the im- a. Definitions consist of cause and
mediate cause. effect ; they also consist of genus
" oil y&p /iovov TO on Set rbv and difference. What is the rela-
bpiariKov \oyov SriXovv, dWa Kai tion of the cause and effect to the
T^v aWiav ivvirapx^iv (cat ifi^ai- genus and difference ? Is the cause
viaBaf vvv Si ttoTTtp aviiirepaaiiaff a generic or a differential element 1
ol \6yoi tSv 'opiav tialv. — De Anima, Or are genus and difference only
ii. 2. constitutive of the formal cause, so
Several questions may be asked that the other causes are neither
with respect to these causal defini- generic nor differential 1
tions. b. This suggests another question :
FOUR KINDS OF DEFINITION. Ill
§ 5. Definition of the immediate is an indemonstrable thesis,
or position of an essence.
§ 6. Real definition, it appears, has three species : '
(1) An indemonstrable statement of the essence.
(2) A deduction of the essence without the deductive
form.
(3) A conclusion of a deduction of the essence.
§ 7. We have now inquired how far essences are demonstra-
ble or indemonstrable, and what essence is demonstrable : and
how many kinds and objects of definition there are, and how
far it proves the essence : and how far demonstration and defi-
nition are identical in object, and what is their relation.
CHAPTER X.
CAUSATION.
§ 1. Science is knowledge of a cause : there are four sorts of
cause: the formal; the material, or the necessitating antece-
dent ; the efficient, or the first excitement : and the final : all of
these appear as intermediates.
What is the relation of the formal to tial connection are described, book i.
the other causes ? for they ought to chap. iv. and xxii. In which of
be contTadistinguished ; and yet in these ways are cause and effect re-
many cases it would seem to be im- lated ? Is the cause a predicate of
possible to give the form or essence the effect, and found in its defltu-
of an object without specifying its tion, as animal in the definition of
material, efScient, or final cause ; as Man ? or is it a subject of the effect,
in the definition of Eclipse, or Thun- and found in its definition, as num-
der, in the preceding chapter. Or ber in the definition of Odd ? Or are
is form equivocal, in one sense ex- some causes related in one way, and
eluding the other causes, in another others in the other, the formal and
including the proximate, efficient, final in the former, the efiicient and
final, or material cause ; as may be material in the latter ? Or are they
implied in the words, 6 ai/rbe Xayog related in none of these modes ? for
uiSi iiiv dvoSei^ig avvtxnQ) <!'^« ^* *l>«s« ^^^™ properly the relations of
opuT/wei chap. IX. species to genus and to specific pro-
c. Cause and effect are essentially perty.
connected, and two modes of essen- ' See Post. Anal. i. 8.
112 FOUR CAUSES.
§ 2. The necessitating antecedent cannot be traced in less
than two propositions '.^ their common intermediate necessitates
the conclusion. Let us take an example : Why is the angle in
a semicircle a right angle ? What antecedent necessitates this
predicate ? Let A represent a right angle : B the half of two
right angles : C the angle in a semicircle. From the proposi-
tions, C is B, B is A, we conclude that C is A ; which means,
that the angle in a semicircle is a right angle : and B is the an-
tecedent that necessitates this conclusion. The interpretation
of symbols resembles verbal definition.
§ 3. The formal cause as intermediate has already been ex-
plained.
§ 4. We inquire the efficient cause when we ask. What was
the origin of the Persian war? Why were the Athenians
attacked ? Because they assaulted Sardis with the Eretrians.
Let A represent war, B unjust aggression, C Athens : A is con-
joined with C, because A and B, B and C are conjoined. The
assault on Sardis, the first movement or original impulse of the
war, appears as the intermediate.
§ 5. When we ask. Why does a man take exercise ? For
health : Why is a house built ? For the preservation of pro-
perty : Health and Preservation are the motive or final cause.
Suppose that exercise is the efficient cause of digestion, and
digestion the efiicient cause of health : and let C represent ex-
ercise, B digestion, A health. In the efficient-cause syllogism
the intermediate that conjoins A with C is the efficient cause B,
which enters into the definition of the final cause A. In the
final-cause syllogism the existence of the fact, that C is B, is
explained by the mediation of A the motive. The propositions
of a sylloigism should be inverted,'^ and then the relation of the
efficient and final causes will be clearer.
' ai viroBiatig Tov ffu/tTTtpair/taroE pics, viii, 12. to yap avTiarpiipiiv
i>Q rb £? qv aXna iari. — Phys. Aus. soTi to fUTaXa^ovTa t6 avfnrkpaaiia.
ii. 3. fiiTO. Twv XoHrwv ipuTtifiaTiav dve-
" The inversion of a syllogism is Xtlv iv twv SoOivTuv. Tlie follow-
when the conclusion and one of the ing is an example. The eye sees be-
premisses change places. For the cause it is of a certain structure ;
meaning of /itTaXpiilSavHp, see To- here the mechanism (B) of the eye
FINAL CAUSE.
113
§ 6. . The terms of the final-cause syllogism do not preserve
the order of occurrence observed in the efficient-cause syllo-
gism. In the syllogism that exhibited the eificient cause, the
middle term. Aggression, was the earliest occurrence : in the
syllogism explaining the motive, the minor term. Exercise, is
the earliest occurrence : the middle terra. Health, the latest.
§ 7. A fact may be necessitated by the material cause, and
yet have a design : ^ as light issues from a lantern in conse-
quence of the material necessity that corpuscles escape through
pores too large to retain them, (if we assume that bodies are
(C) is the efficient cause of sight (A) ;
and we have the following syllo-
gism :
all B is A
all C is B
. . all C is A.
But the eye is of a certain structure
in order that it may see.: sight is
the final cause of the mechanism of
the eye. In the syllogism by which
this is expressed,
all A is B
all C is A
.-. all C is B,
the minor and conclusion of the
former syllogism have changed
places.
• A lantern (A) emits Ught (C)
because it is of a porous material
(B), and in order to guide us in the
dark (D). The proposition, A C,
may be proved by either of the mid-
dles, B or D ; the proposition, A D,
may be proved by the middle B, and
the proposition, A B, may be proved
by the middle D. The difficulty of
reconciling the efficient and mate-
rial with the final cause, a question
which is here so briefly dismissed,
has been one of the chief points on
which the schools of philosophy
have split, some adopting the ma-
terialistic, others the spiritualistic
theory. Kant attempts a recon-
ciliation in his Critic of the Judg-
ment. See Plato, Phsedo, § 106 >
also Trendelenberg's Logic. The
conclusion deducted fi-om a final
cause indicates the necessary con-
dition for realizing a proposed end,
and is said to possess an hypo-
thetical necessity, tovto S" etrriv
(Kffwfp l^ VTToQkatiaQ. &<nrep yA-p,
iirei Sti axiZ^iv Tif ireKiKei, ccvdyKr)
aKKripbv ilvai, li di (TKXtipbv, X"^"
Kovv fi eiSripovv, ovtijiq xal iTriiSr)
rb ffwiia opyavov, evSKa yap rtj/off,
avdyKH) ToiovSi ilvai Kal ix ToiuivSl,
ti ixeXvo iarai. — De Part. An. i. 1 .
oiov^ Slcl ri b 7rpuj}v rotoffSi ; '67r<dQ
ToSl Kal 'ivsKa rovSi, tovto fikvToi
Tb ov 'ivcKa advvaTov yeviaOaL dv
fvfl mSripovg y' dvdyKt] dpa aiStj-
povv elvai, el trpiiov iffToi Kal Tb
epyov avTov. s^ vTroBkffetoc ovv Tb
ivayKoiov. — Phys. Ausc. ii. 9. Prac-
tical deliberation proceeds from the
final to the discovery of the efficient
cause, and is based on a definition
of the former, ij dpxv "i"'^ I'ov
bpttTfWv Kal Tov \6you. bpcffafievt^
yap rb Ipyov rov irpieiv, 'on Siaipc-
ai£ TOiaSi, avTr) S" oiiK tOTai, tl fifi
'i%u bSovrag roiovffll, ovtoi S' ov, ei
/irj atStipovg. — Ibid. Compare Nic.
Eth. vi. 12.
114 FINAL CAUSE.
transparent by the transmission of light through their pores,)
and in order to guide us in the dark. There is no reason why
the origin of a fact as well as its permanence should not be due
to two causes : as for instance, in the case of thunder : it is
quite possible that the roar and hissing may be the necessary
effect of the extinction of fire in a cloud, and that it may be
designed, as the Pythagoreans said, to strike awe into the in-
habitants of Tartarus. Cases like this are very numerous in
natural productions and processes : for there are two kinds of
nature ; one a necessary agent, the other acting with design.
§ 8. Necessity is of two kinds ; Nature, or the internal im-
pulse, and Violence, opposed to the internal impulse : a stone
is necessitated to move upwards and downwards, but not by
the same kind of necessity.
§ 9, Some productions of human intelligence, as a house or
a statue, never arise by chance or by necessity, but always by
design : others, as health or preservation from danger, may
result from chance. Contingencies, when not produced by
chance, and when the end is good, are most obviously designed
by nature or man. Chance is inconsistent with design.
CHAPTER XII.
SUCCESSION OF CAUSE AND EFFECT.
§ 1. As existing effects are explained by existing interme-
diates, so past, present, and future effects are explained by past,
present, and future intermediates. i The moon will be eclipsed
because the earth will intervene ; was eclipsed because the
earth did intervene ; is eclipsing because the earth is interven-
ing. Suppose that ice is water solidified : and let C be water ;
A solidified ; B the intermediate, complete departure of heat :
' Perhaps ov should be translated ex^i Svalv ipQaXg dd t&q yuviag
eternal; for that which is eternal laag- dW 'Siibig kari n r^e aidwrri-
may have a cause. ArifioxpiToe dk roe TavTr/s 'irepov curiov rCiv jiiv-
Tov dei oi(c ajiol dpxnv Zrireiv, \k- toi dpxHv oitk tariv ertpov alnov
yiDvovK 6p9ac- Kal yap rb rpiytavov d'iSiwv oiaSiv. — Phys. Ausc. viii. 1.
LOGICAL SEQUENCE OF SUCCESSIVE EVENTS. 116
Ice forms while B is happening ; has formed when B has hap-
pened ; will form when B shall happen.
§ 2. Such effects and causes, whether past, present, or future,
are simultaneous both in occurrence and duration : other causes
and effects are not synchronous, but successive : past effect
succeeding past cause ; present effect present cause ; and future
effect future cause.
If both events are past, the antecedent may be inferred from
the subsequent, and the intermediate will also be a past event.
But the subsequent cannot be inferred from the antecedent :
for whether the interval between them is definite or indefinite,
it is false to assert the subsequent before the interval has
elapsed.
There is the same relation between two present or two future
events.
§ 8. From a past occurrence, as minor, we cannot infer a
future occurrence, as major : for the intermediate must be
homogeneous to minor and major, whether past, present, fu-
ture, or eternal ; and the same middle cannot be homogeneous
both to past and to future. Besides, whether the interval is
definite or indefinite, before it elapses the latter cannot be
asserted.
§ 4. It should be inquired, what is the principle of continuity
between present and past events : or rather, it is clear that two
past events are limits or atoms, and. resemble points in their
indivisibility and discontinuity : and that, as lines contain an
infinite number of points, so present of past events ; and the latter
as well as the former are incapable oTcontinuity.
This subject, however, must be treated more fully in the
general theory of production.
§ 5. When the rise of events is successive, the primary cause
is immediate. Let A, C, D, be successive past occurrences ; then
C, compared with A, is a principle or intermediate, as nearer to
the Now, or present moment, the beginning of time. If D has
occurred, C has occurred ; and if C has occurred, A has oc-
curred : therefore, if D has occurred, A has occurred, by the
intermediation of C. However long we proceed in this manner,
we shall never have filled up the interval with immediate links,
but there will always be room remaining for infinite intercala-
116 NATURAL CYCLES AND CIRCULAR PROOF.
tions ; there being, as we said, no continuity between events
that have past. Yet the Now furnishes us with a primary and
immediate point of departure.
§ 6. The same is true of future events : if the subsequent D
takes place, the antecedent A will have taken place, as may be
proved by the intermediate C. If D takes place, C will have
taken place ; and if C takes place, A will have taken place :
therefore, if D takes place, A will have taken place. This series
also is infinitely divisible, for future events are discontinuous :
yet here, too, the ultimate point of departure is immediate.
§ 7. This may be exemplified. If a house was built, the in-
termediate laying of the foundation proves that stones were
shaped:* if a house was built, the foundation was laid; if the
foundation was laid, stones were shaped : therefore, if a house
was built, stones were shaped.
Again, if a house shall be built, the same term will serve as
intermediate to show that stones will be shaped.
§ 8. Nature presents a perpetual cycle of occurrences -.^ this
may be explained in a syllogism whose middle and extremes are
convertible : then all the three propositions may be obtained by
reciprocal generation, each appearing at one time as premiss, at
another as conclusion, the reasoning proceeding in a circle.
The following phsenomena furnish an example. When the
earth is wet with rain, an exhalation rises ; when an exhalation
rises, a cloud forms ; when a cloud forms, rain follows, and the
earth is saturated : so that the same term recurs after a cycle of
transformations. Every occurrence has another for its conse-
quent ; and this consequent another, and so on, till \^ 3 are
brought round to the primary occurrence.
§ 9. In some occurrences the attribute is commensurate to
the subject ; in others, as the growth of a beard, the attribute is
' De Gen. et Corr. ii. 10. yiviine> ^vayKri TrepiKVKKeiv Kai it'a-
" ri^ Xinrofikvi^ Tpoviji avvejrXrj- Kajiirriiv . . . avriarpifuv Spa civdy-
piiiae TO '6\ov o 9tbs, ivBiXsxrj ttoijj- kij tarai. — Ibid. li. 10.
aac rfiv yivtmv . . . Sib Kai raWa, Set Si vor)trai tovtov &(nrcp rrora-
offa jUcrrt^aXXtt dg dWrjXaj fitfietTat fibv piovra KVK\(p dvo) Kai KaTtt)' Kai
rijv KiVXij) (j)opdv iiovri yap r) KiiKXif) tovt MeXexh iOiXu yiyvfoBai. —
<rvvexv£' — De Gen. et Corr. ii. 9. Meteor, i. 9.
el apn rivbg i? dt'dyKTjg cnrXhtg t]
DEFINITION. 117
only general, not universal : the latter results from a general
intermediate. If A were commensurate to B, and B to C, A
would be commensurate to C ; that is, predicated at all times of
all its individuals. By hypothesis, C and A are only generally
conjoined; therefore the intermediate and extremes are only
generally conjoined : therefore there are immediate general
propositions.
CHAPTER XIII.
ESTABLISHMENT OF DEFINITION.
§ 1. Having explained how essence is defined, and how far it
is definable or demonstrable, let us examine how its elements
must be discovered.
Some universal predicates are more extensive than the species,
though confined to the genus ; entity is predicable of the triad,
and of other subjects beyond the genus Number ; but Odd,
though predicable of other subjects, such as the pentad, is pre-
dicable of nothing beyond the genus Number. The primary
combination of such predicates that is not wider than the sub-
ject is its definable essence. A triad is a number, is odd, is
prime, whether as not measured by a single number, or as not
compounded of several numbers. The combination of these
elements is its essence ; for though the second is common to all
odd numbers, and the last to the duad ; the whole combination
is predicable of none but the triad.
§ 2. As commensurate and essential predicates are necessary,
this combination of predicates to the triad is necessary. If it is
not the whole essence, it must be a genus : but then it would
be more extensive than the triad; assuming that this is the
character of a genus. Assume further that the ultimate or
lowest essential predicate, that is, an essential predicate incapa-
ble of further subdivision, is the essence ;' and that combina-
' Such an assumption makes the proof Dialectical, not Demonstrative.
See chap. vi.
118 DEFINITION.
tion of elements must be th.e definition of the triad, or any other
subject which satisfies these conditions.
§ 3. In treating of any subject-matter, such as number or
figure, we should obtain by division the lowest and indivisible
classes of its elementary members — the duad, the triad, the
straight line, the circle, the right angle ; and after defining
these classified elements, and observing the category of quan-
tity, quality, or the like, to which they belong, proceed to elicit
their peculiar properties, developing them by means of the com-
mon canons or axioms. i For the attributes of what is com-
pounded of the elementary may be deduced from these defini-
tions ; for the essence of the elementary is the ultimate ground
of the attributes of the class, which are essentially connected
with the elementary alone, and thence imparted to the com-
pound.2
§ 4. Division by difierentise is useful ; though, as said above,'
the essence cannot be deduced or demonstrated, but is finally
assumed just as much as if no division had preceded. It is im-
portant, however, to determine in what order the elements
should be arranged ; whether as animal, tame, biped, or biped,
animal, tame. Every object is the union of two elements;
animal unites with tame, and the result uniting with a new
difierentia composes the essence of Man ; and the right order in
which the new elements should be assumed, so as to unite the
right genus to the right differentia, can only be learnt by
Division.
§ 5. Again, this is the only security against omitting any
elements of the essence. After we have assumed the primary
genus, unless we subdivide by proximate differentiae, the divi-
sion cannot be exhaustive ; whole-winged, for example, and
divided-winged is not an exhaustive division of animal, but of
winged animal. The primary diflferentia of animal, or of any
other genus — whether coordinate to animal, or, like fish and
bird, subordinate — must comprehend every individual, whether
animal or fish or bird : and then we may be sure that we
have made no omission in the elements of the essence, of which
we otherwise should have no guarantee.
' Post. Anal. i. 32. = Eth. Eudetn. ii. 6. ' Chap. v.
DEFINITION. 119
§ 6. Definition and division, some assert, suppose universal
knowledge, since an object is only known when we know its
contradistinguishing diflFerentiae ; and its contradistinguishing
difierentise cannot be known, unless we know all the objects
from which it is contradistinguished ; for, say they, objects are
distinct or identical by the presence or absence of differentiae.
But it is not true that every differentia destroys identity. Ob^
jects identical in kind may possess unessential differentiae. Se-
condly, if you divide by contradictory differentiae, and know to
which division the object under discussion belongs, it is quite
superfluous to know what objects possess the other differentia;
but as soon as we reach an indivisible class, the exhibition of
the essence is complete. It is no petition or mere hypothesis to
assert that every object falls under one or the other of two con-
tradictory divisions j^ for contradictory differentiae must exhaust
a genus.
§ 7. Three rules must be observed in defining : the elements
must be generically essential ; they must be arranged in order ;
and they must exhaust the essence.
As there are dialectical topics for establishing an accident, so
there are for establishing a genus f and these will aid us to satisfy
the first requisite.
§ 8. To determine the order, we may assume that the pri-
mary genus is that which is universally predicable of the others,
and of which the others are not universally predicated. Such
an element there will be found to exist : and the order of the
rest may be determined by the same criterion ; for when a prior
class is excluded, the next foUowiftg is primary of the remainder.
Exclude the first, and the second is primary ; exclude the first
and second, and the third is primary.
§ 9. The enumeration will be complete, if we divide the pri-
mary genus by exhaustive differentiae, and the successive sub-
genera in like manner, till we ultimately reach a genus which
has no further differentia ; or, till the subject's ultimate genus,
combined with the ultimate differentia, is susceptible of no
' This assertion is the Axiom. method of Opinion, oaght to be em-
" This is the chief flaw in Aristo- ployed in establishing scientific prin-
tle's Logic : for some more rigorous ciples.
method than the Dialectical, the
120 DEFINITION.
further division. ' Nothing is superfluous, for all the elements
are suhstantial ; and nothing is omitted : if any element is left
out, it must be either' a genus or a difierentia : neither supposi-
tion is possible ; for the genus is the primary class, either alone,
or in combination with the difierentiee : and the series of diifer-
entise was exhausted, as the last we came to was by hypothesis
indivisible.
§ 10. To find a definition, we should first look for the point
of identity in a set of similar individuals that have no contra-
distinguishing differentia ; and then examine a second set,
distinct from the former in species, but identical in genus : and
after finding, the point of identity between the members of the
second set, and so of a third, compare the specific characters
thus obtained, and see if they present any higher point of iden-
tity: and if we find a single all-pervading character, this will
be the definition ; if not, the subjects examined are not one, but
several. For instance, to define magnanimity, we should ex-
amine what quality is common to a set of persons known to
possess the attribute of magnanimity. Alcibiades, Achilles, and
Ajax were magnanimous : in what did they agree ? In impa-
tience of dishonour ; which made one a traitor, roused another's
wrath, and drove another to self-slaughter. Again, in what did
a difierent set, Lysander and Socrates, agree ? In equanimity in
adversity and prosperity. What element is common to these
characters, equanimity in vicissitudes, and impatience under
dishonour ? If there is nothing in common, there are two dis-
tinct kinds of magnanimity.
§ 11. Definition must always be commensurate: for a physi-
cian does not prescribe for a single eye, but for a whole genus
or species. Particular definition, however, is easier, and there-
fore should precede as a preliminary. Equivocation is more
readily detected in dealing with particulars than with univer-
sals : and perspicuity is as indispensable to definition as se-
quence to demonstration. To attain this, therefore, we should
begin by defining separately the subgenera ; similarity of colour,
similarity of figure ; acuteness of sound, acuteness of figure ;
and afterwards proceed to similarity and acuteness in general,
with an especial jealousy of equivocations.
As metaphorical reasoning is unscientific, so is metaphorical
EXPLANATION OF PHENOMENA; 121
definition ; whether the words we define, or the words by which
we define, are metaphorical ; for this would necessarily produce
metaphorical reasoning.
CHAPTER XIV.
EXPLANATION IS RESOLUTION INTO HIGHER OR
ANTECEDENT LAWS.
§ 1. To solve the problems of a science, our preliminary inform-
ation should be collected and arranged as follows : > we should
divide wholes into their parts, and genera into their species ;
and place first the attributes of the whole genus ; if the inquiry
is zoological, the characteristics of the whole animal kingdom ;
next the characteristics of the immediate subdivisions ; of the
whole subgenus bird for instance ; and the remainder in like
manner. This will enable us to deduce or explain the charac-
teristics of the subgenera. Let A represent animal, B animal
characteristics, C D E particular animals, as man or horse.
Then A wiU be the reason why B is predicated of C.
§ 2. We should not confine our observations to commonly
recognized genera, but endeavour to detect other generic cha-
racters, and ascertain what predicates are attached to them,
and to what subjects they are attached. A class of animals is
homed, and characterized by a ruminating apparatus and the
absence of teeth in the upper jaw. If we know what animals
are the subject of this predicate, the possession of horns, this
character,^ the possession of horns, is the cause and explanation
of their possessing the other characteristics.
§ 3. We must also observe analogies : there is no common
' The collection of premisses, whe- iii. 14. The explanation here given
ther, as here, Scientific Theses, or is, that the horns exhaust the mate-
Dialectical Organa, oi' Rhetorical rial that might have formed, the up-
specific data, is expressed by the per teeth ; and, as thereby the mas-
word hUyuv or iKXaii^avav. To- tication is incomplete, to assist the
pics, i. 12; Prior. Anal. i. 27 ; Rhet. digestive process, nature provides
jj_ 22_ the ruminating apparatus, a kind of
'' See De Part. Anim. iii. 2. and secondary stomach.
122 RELATION OF CAUSE AND EFFECT.
name for the spine of fish, the pounce of the sepia, and the
common bone, but they all have the same concomitant attri-
butes, evincing a unity of nature.
§ 4. Identity of problem is constituted by identity of the ex-
planatory intermediate ;i as several problems are explained by
the development of an opposite by its opposite ; and here the
intermediate, though the same in genus, may differ in subject
or in mode. The echo, the image in a mirror, the rainbow,
are caused by refraction, generically the same, but different in
species.
§ 5. Or problems are identical, if the explanatory middle of
the one is subordinate to the explanatory middle of the other.
The Nile swells at the close of the month, because the weather
is stormy ; the weather is stormy because the moon wanes :
these causes are subordinate.
CHAPTER XIV.
RECIPROCATION OF CAUSE AND EFFECT.
§ 1. As the presence of an efiect implies the presence of its
cause : for if the fall of the leaf and the moon's eclipse do not
imply the leaf's broadness and the earth's interposition, their
origin must be due to other causes : and as the presence of the
cause, the broadness of the leaf, or the interposition of the
earth, implies the presence of the efiect, the fall of the leaf or
the moon's eclipse : the cause and efiect are simultaneous, and
the cause is deducible from the efiect as well as the efiect from
the cause. Let A be the fall of the leaves, B broadness of the
leaves, C the vine. Because A is predicated of B, and B of C,
therefore A is predicated of C, and B the intermediate is the
cause. Again, the broadness of the vine-leaves is deducible
from their annual fall. Let D be broad-leaved, E shedder of
leaves, F the vine. All F is E, and all E is D, therefore all F
' See the Meteorics, where he proposes to explain a great variety of
pheenomena by very few causes.
RELATION OF CAUSE AND EFFECT. 123
is D. In this case, however, the intermediate E is not the
cause, for causation implies priority, and cannot be reciprocal.
As interposition is the cause of eclipse, and not eclipse of inter-
position, and a reasoned or explanatory proof employs the
cause, a deduction of the latter kind is not a reasoned proof,
but only a proof of fact. Interposition is the cause of eclipse,
and not vice versa, for it enters into the definition of eclipse,
and renders it cognizable.
§ 2. If, however, the same term may be the primary predi-
cate of several subjects, may not the same effect arise from
severed causes ? Let A be a primary predicate of both B and
C, and B of D, and C of E. A then is a predicate of D and E
by the respective causation of B and C. The existence, it would
appear, of the cause involves the existence of the effect ; but
the existence of the effect only involves the existence of one
among several possible causes. If, however, the theorem is
commensurate, the effect will be commensurate to the cause.
The fall of leaves must be explained of its commensurate sub-
ject, whether a whole class or a species, whether the whole
vegetable kingdom or a particular province : so that the cause
or intermediate will be equal in extent and convertible with the
effect or major. If the fall of leaves is produced by coagula-
tion, wherever there is a fall there must be coagulation, and
wherever there is coagulation of sap there must be a fall of
leaves.
§ 3. There is only one cause from which an effect can be de-
duced, if the demonstration is essential ;^ for then the middle is
' "The ideal limit, therefore, of modes of production may be resolved
the explanation of natural phseno- into another, or that all of them
mena (towards which, as towards may be resolved into some more
other ideal limits, we are constantly general mode of production not hi-
tending, without the prospect of therto recognized. But when the
ever completely attaining it) would modes of production are reduced to
be to show that each distinguishable one, we cannot, in point of simplifi-
variety of our sensations, or other cation, go any further . . . Accord-
states of consciousness, has only one ingly the greatest achievements in
sort of cause As long as there physical science have consisted in
are several known modes of produc- resolving one observed law of the
tion of a phenomenon, so long it is production of motion into the laws
not impossible that one of these of other known modes of production.
124 RELATION OF CAUSE AND EFFECT.
the definition of the efiect or major. The same effect is sus-
ceptible of many deductions by sign or accident : both the ma-
jor and the minor premiss, both the conjunction of effect and
cause, and of cause and material, may be accidental ; but such
propositions are useless in a scientific theorem.
§ 4. The premisses resemble the theorem ; if it is equivocal,
the premisses are equivocal ; if it is incommensurate, they are
incommensurate. The cause of the convertibility of a propor-
tion is both different and identical for proportional lines and
proportional numbers ; different so far as they are lines and
numbers ; identical so far as they receive the same increments.
§ S. If one cause can be given why colour is similar to
colour, and figure to figure, it must be equivocal ; for similarity
of figure is analogy of sides and equality of angles ; and simi-
larity of colour is production of the same sensation, or whatever
else may be its definition.
§ 6. If effects are analogous, the intermediates by which
they are deduced are analogous.
§ 7. There is a reciprocal sequence between the major, the
middle, and the minor terms, the effect, the cause, and the ma-
terial. The major is more extensive than any particular minor,
but equal to the universal class : the equality of exterior angles
to foar right angles is more extensive than triangle or square,
but equal to the whole class of plane rectilinear figures : and
the relation of the middle to the extremes is similar.
§ 8. The middle is the definition of the major; therefore
definitions are the basis of a science. The fall of the leaf is an
attribute of the vine, but more extensive ; of the fig, but more
extensive : it is co-extensive to some class in which they are all
embraced. The primary intermediate defines the fall of the
leaf, the attribute or major : not Broad-leaved, the primary in-
or the laws of several such modes shown to be produced by electrl-
into one more general mode ; as city ; when the motions of fluids in
when the fall of bodies to the earth, a lateral direction, or even contrary
and the motions of the planets, were to the direction of gravity, were
bi'ought under the one law of the shown to be produced by gravity;
mutual attraction of all particles of and the like." — System of Logic,
matter; when the motions said to bookiii. 14,
be produced by magnetism were
RELATION OF CAUSE AND EFFECT, 125
termediate next the subject, which is only a class including all
leaf-shedding trees : but the intermediate next the effect or
attribute — coagulation of sap, or whatever else it may happen
to be. Leaf-shedding is defined by the coagulation of the sap
at the junction of the stalk and stem.
§ 9. To examine with symbols the incommensurate sequence
of cause and effect, assume the propositions,
all B is A
all D is B:
where A the effect is universal to B the cause, but not its pri-
mary or coextensive universal : and B the cause is universal to
C the subject, but not its primary or coextensive universal.
As B- is not the only cause of A, let us assume otjjer propo-
sitions :
all C is A
all E is C;
where the terms are similarly related. If neither B nor C is
commensurate to A, they must be mutually exclusive : for any
genus that contained all the causes of A would be commensu-
rate to A, which is contrary to hypothesis.
The same effect, then, may be produced by different causes, but
only in subjects specifically different. Longevity may be due
to the absence of gall in Quadrupeds : in Birds to the predomi-
nance of solids, or whatever else the cause may be.
§ 10. If a subject does not fall at once under the term indivi-
sibly connected with the attribute, but is separated from it by
several intermediates, all these intermediates are causes of its
possessing the attribute.
§ 11. Which is properly called its cause? the intermediate
immediately adjoining the universal or attribute, or the one
immediately adjoining the subject? The one adjoining the
subject is the cause that the primary or subject falls under the
universal or attribute. If D is C, and C is B, and B is A ; C is
the cause that conjoins the effect A to the subject D, because it
conjoins B to D ; B is the cause that conjoins the effect A
to the subject C; and B is the cause of its own conjunction
with A.
[ 126 }
CHAPTER XVI.
THE ORGAN OF PRIMARY TRUTHS.
§ 1 . Suet is the nature and origin of syllogism and demon-
stration, and, what is the same as the latter, of demonstrative
science.
Let us now proceed to consider the method and the faculty by
which elementary principles are recognized. Demonstrative
science, as we saw, is based on a knowledge of primary im-
mediate principles. Is the mode of knowing the immediate
identical with the mode of knowing the mediate ? Is it Science,
or something different in kind? Are the appreciating faculties
acquired, or are they innate, though unobserved ?
§ 2. They cannot be innate : we can scarcely have a know-
ledge more perfect than demonstration, and yet be unconscious
of it. If they are acquired, we saw, when treating of demon-
stration, that we cannot learn and acquire knowledge without a
basis of previous knowledge. As, then, they are neither in-
nate, nor acquirable without a basis of previous knowledge
and perceptions, some developed power must be innate of
inferior perfection and excellence to the faculties of the im-
mediate.
§ 3. Such we find in all animals : all have an innate percep-
tive power which we call Sense. In some the sensation is tran-
sient; and these have no knowledge, at least of the objects
whose impression is transitory, beyond sensation. Others retain
the sensation, and these are subdivided ; for in some of them a
number of permanent 'sensations develop^s an intellectual con-
ception.
On sensation, then, ensues memory ; and on many memories
of the same fact Experience : for many similar memories are
one Experience : on Experience, or the whole unchanging uni-
versal that has settled in the mind, the all-permeating One be-
side the Many, ensues the beginning of Art and Science; of
ORGAN OF PRIMARY TRUTHS. 127
Art if the end is production, of Science if the end is truth.» The
faculties, then, are neither innate and originally developed, nor
preceded by any higher cognizant power, but by Sense.
§ 4. In a battle, when an army is taking to flight, first one
man makes a stand, and then another, and another, till they re-
cover their original order :* the soul is adapted for undergoing
a similar process : and we may now repeat more distinctly what
we said before. So soon as an individual makes a stand in the
mind, we have the primary or lowest universal ; for, though
sensation perceives Callias, the individual, sense perceives Man,
the universal : in these lowest universals, higher universals
make a stand ; and finally the indecomposable and highest uni-
versals : first a kind of animal, then animal, and then a higher
genus. Man's knowledge of the elementary, it appears, is
inductive ; for the way that sense imparts the universal is in-
ductive.
§ 5. Our intellectual faculties are either fallible, as Opinion
and Reasoning, or infallible, as Science and Reason. As all
science implies conclusion, principles are not objects of science.
As principles are more evident than conclusions, and no power
except Reason has greater light and insight than Science, prin-
ciples are the objects of Reason.
Again, as the basis of demonstrated truth is not demonstrated
truth, so science is not the basis of science. If Reason is the
only infallible faculty besides Science, Reason must be the
' With ^pe/ifiaavTog tov Ka96\ov fiiv KaBoKov rjpeiiovira /laXKov, »/ Si
compare, rip ydp ^pe/iriaai Kal aTrj- ov. — De Anima, iii. 11.
vai Ttfi' Siavoiav iiriaraadai Kal ' The drift of this simile is ob-
^poi'cti' Xcyo/ieda , . . Tif ycip Kadi- seure : it may mean, that as order
araaBai riji/ i^x^v Ik Trig •h^iKrJQ succeeds to the disorder of flight,
ipeTrjg ijipdvifiSv ri yivcrai Kal ini- so the ordering ideas succeeds to the
arrjiiov . . . KaBiararai Si Kal iravi- confusion of pheenomena ; and as
rai TTJg rapaxije totc fiiv iiirb rrjg the routed army could not have as-
^vaciog Tore S" vir' dWoiv. Phys. sumed Its second array but for its
Ausc. vii. 3. ruv aKivrjruJv '6pii>v Kal former organization, so the regu-
vp&Tiav. Jfic. Ethic, vi. 11. 'iartjai lating ideas could not appear in the
yelp Xtyuv t^v Siavoiav Kal b dKov- mind, unless there were in nature
aag ^pk/uiatv. — De Interp. 3. behind the confusion of pheenomena
afi^ot Kivovffiv al So^aif &\\' rj an original order and law.
128 ORGAN OF PRIMARY TRUTHS.
basis or beginning of Science :* and the beginning of Science
bears the same relation to the basis or beginning of truth, that
the whole body of science bears to the whole body of truth.
' a'pX^" ^inaTriiitig clvai nva fiev jiva, iv Si iiiXti Sitatg, iv Sk
^afiiv, y Toiig '6povc yvuipU^o/iev. — avWoyia/iif ri 'iv irpoToaiQ a/ttaoe,
Post. Anal. 1. 3. i) apx4 iv ^dpu iv S" linijrijiiy 6 vovg, — Ibid. i. 23.
APPENDIX
APPENDIX A.
AXIOMS.
§ 1. An Axiom is a principle not limited to any one depart-
ment of nature, but equally applicable to every subject-matter.*
The leading Axiom is expressed under various formulae. In the
Metaphysics we have,* One of two contradictories must be true ;
and. The same thing cannot be and not be. In the Prior Ana-
lytics,* The same subject cannot have contradictory predicates ;
and, Every subject must have one of two contradictory predi-
cates. In the Treatise on Fallacies,* Things which are the same
as the same are the same as one another.
§ 2. It is clear that if this principle were not true, if it were
possible that the propositions, A is B, and A is not-B, could
stand together, there could be no reasoning and no thought.
Accordingly those who denied the possibility of Knowledge or
Philosophy, in order to do their work thoroughly, selected this
principle as the object of their attack. To effect its overthrow
various doctrines of celebrated philosophers were brought to
bear.
Heraclitus, for instance, had said that all nature is in a per-
petual flux, so that nothing is in the same state for two succes-
sive moments.^ From this it would follow that neither of two
contradictories could be predicated with truth of any subject.
* Koivov. — AndX, Post, passim. * rd. kvl Kal ravTi^ ravrd, Kal d\~
" irav avafKoiov r) ipavai ri airo- X^Xotg diiovjuv ilvai raira. — Soph.
ifidvai, Kai dSvvaTov li/ia ilvai Kal Elench. 6. Perhaps the most au-
ft^ tlvai. — Met. iii. 2. cient formula is the line of Parme-
^ (pane K"' airoipame oix vv&p- nides : oii yap firjiroTe tovto Says,
Xovaiv al AvTixdiuvai a/juz rip aiiTig. elvai /*^ kovra. — ^Plato, Sophistes.
. . . Kara iravrbs ivbg v ijictaiQ n * Met. iv. 5.
anoipane a\i)6J7£. — Prior. An. i. 40.
13-2 AXIOMS.
Anaxagoras held that the ultimate elements could never be
entirely separated ;i that nothing in nature was pure or simple,
or excluded opposite elements, but received its denomination
according to the predominance of particular ingredients. It
follows, that neither of two contradictories can be predicated
absolutely of any subject. He maintained also, that whatever
seems is true ;* an assertion similar to that of Protagoras, who
taught that man is the measure of reality, which meant that
opinion is the criterion of truth ;* and, as the same objects pro-
duce different sensations and opinions in different men, it was
inferred that truth may be self-contradictory.
To avoid the consequences of the doctrine of HeracHtus,*
Plato, who came from this school, maintained the existence of
immutable Ideas.
§ 3. As all the sciences alike assume the truth of the Axioms,^
it does not appear to which of them the discussion properly
belongs, and this is proposed as a question in the Metaphysics;
where it is decided, that, as they are true of all Being, they
belong to the science of Being, and accordingly they are dis-
cussed by Aristotle in the Metaphysics. ^
§ 4. The Axioms are indemonstrable ; for it is impossible
^ ofiov TTOLvra ;3^p^juara, uiffre lit]- also Met. iv, 5. Bat (Tot, lav Ti ^ovKy,
Slv aXtjBSiQ tv VTrdpxuv. — Met. iv. kdv Te fjf^, dveKTsov '6vri fiirpty, —
4. ficfiixBai irdv iv Ttavri. — Met. Plato, Theaet. § 64. airapKr] exa-
iv, 5. kv navri TravTog tlvai jioipav, <ttov eig ^p6v7j(TLv iTToiei. — Ibid.
— Met. xi. 6. ilKiKpiviog /tiv yap % 69.
oXov XevKbv jj )ik\av ovk Avai, '6tov * {liar, tmsp iTriarriiiri rivbg iarai
5k wXeiaTov EKatrrov ix^^j tovto do- Kai ^povTjfftgj eTEpug SeXv riv&g 0u-
Kelv elvai rrfv (pvmv Tov irpdyiiaTog. aug tlvai^irapcL rag aiaOtiT&g /je-
— Physic. Ause. i. 4. ore ydp ovSiv vovaag' ov ydp elvai tGv piovTiav
rjv dTTOKEKptfjtsvoVf 6i]\ov tbg ovSkv kTTHTTrj^rjv. — Met. xiii. 4.
ijv aKrjOeg e'nnXv Kara rrjg oiaiag •" rrdaai ydp at diroSeiKTiKal XP<^V-
sKeivr/g. — Met. i. 7. rai roTg d^iii/iamv. — Met. iii. 2.
^ ' Xva%ay6pov Si Kai diroipdiyjia * i'Trti SriKov on y ovra virdpxu
livrj/jtovEVETat irpbg tGiv iraipfiyv rt- irdffi, tov ttEjOi rb ov y ov yvo}piZov~
vdg, on rotavra avroig rd bvra, ola Tog Kai -Trepi rovTbiv itrrlv ri 9eo}pia,
av iiroXd^Mm. — Met. iv. 5. — Met. iv. 3. on fiiv ovv tov fiXo-
" sKHvog tft) trdvTiiiv tlvai xpriiid- aoipov Kai rov jrtpi ndarig Trjg ovaiag
TiDv fitrpov TOV dvBpwjrov ovSiv Beuipovvrog y TrtipvKe xal irtpi rSiv
ETEpov Xiyiav, t) ri Sokovv EKoiffTt^ avXXoy WTiKmv dpx&v iffTiv E-jTLffKS-
TOVTO Kai Eivai. nayiiag. — Met. xi. 6 ; \j/aa9ai, S^Xov. — Ibid.
AXIOMS.
133
that every truth should be demonstrated, as this would imply
an infinite series of demonstrations ; and there is no truth that
has a higher claim than the Axiom to be received on its own
evidence.^ To deny them is to deny the possibility of reason-
ing ;2 to attempt to prove them would be to make a petitio
principii, as they are involved in all proof.^ Besides, all De-
monstration implies a subject of which a predicate is demon-
strated, and Axioms whereby it is demonstrated ; and how can
the Axioms themselves be susceptible of this further analysis ?*
They can only be dialecticaUy maintained ; that is, if the oppo-
nent grants us any premisses, it would not be difficult to show
a number of absurdities that flow from his Thesis -.s and then
he is responsible for the petitio principii, as the propositions are
of his own concession.^ The mode of argument should be, to
demand a verbal definition of any subject, 'and then to show
that it has some predicate, and excludes its contradictory.^
The doctrine of the Sceptics is self-destructive ;8 for if we
* avTTj 5* airaffuiv kffri ^i^aioTari}
rdv 'Apxwv. — Met. iv. 3.
oil yap iariv Ik irurroripae dpxvs
avTov TOvTov TTOirfffatTOai tov otjX-
\oyt(7ii6v. — Met. xi. 5.
£t Si rivinv iiri del Zi]Tiiv aTroSa-
^iv, Tiva d^tovixtv eZvai ftaWov roi-
avTi]v dpxvv, ovK &v e%ot€v eiireXv.
Met. iv. 4. \6yov y&p ZiTovaiv S}v
oliK tan \6yoQ' diroSti^e<og yap <ipx4
OVK dit6But,iQ EffTLv. — Met. iv. 6.
' dvripijTai TO diaXiycoBai irphQ
oKKiiKovQ' Kard, Sk ttiv dXijOetav Kal
wpbg avTov ovSkv ydp ivSkxtTai
voiiv iit)9iv voouvTa iv. — Met. iv.
4.
^ 6 diroSsiKvvtitv &v S6^si€v airii-
aQai rb iv dpxy. — Met. iv. 4.
* ti S" diroSuKTiKri Trtpi aiirdv loTi,
Seijasi rt ykvOQ tlvai viroKetfievov,
Kai T& iiiv irddri, ra S" dKui/iara
airSv dvaysri yap Ik rivutv tlvai,
Kal TTtpi Ti, Kai nviav, rijv diroStii,iv.
—Met. iii. 2.
' iari S" diroSil^ai iXiyKTiKSis, av
iwvov n Xiyy o dji^iafitiTCiv. — Met.
iv. 4.
oi p<j,Siov SiaXvaai fx^ tiBbvtidv n xai
TOVTiiiV flTJKETl \6yov diratTOVVTUV ,
fir/Skv yap TiSivree dvaipovtri rb Sia-
XiyEdQai xai 'dXuig Xoyov. — Met. xi. 6.
^ aiTwg ovx b diroSuKvig dXX' 6
virop-kvuiv' dvaipwv yap Xoyov viro-
fisvH Xoyov. — Met. iv. 4. Compare,
Alii aatem negabant se pro hac evi-
dent!^ quidqaam priores fuisse dic-
turos ; Bed ad ea quae contra dice-
rentur dici oportei-e putabant. —
Academioa Priora, ii. 6.
' dpxv ^^ irpbg a-jravrag rovTovg
i% bpia/iou. — Met. iv. 7.
oJcrre k^ bpuTfiov SioXsktbov. — Met.
iv. 8.
dpx^ Sk "Trpbg liiravTa tcl ToiavTa
TO d^iovv atiiiaivuv ye n. — Met.
iv. 4.
* au/iPaivu S^ sal rb BpyXXov/ii-
vov irdai roXg rowvToig Xoyoig' av-
Toig kavToiig dvaipuv. — Met. iv. 8 j
also Met. xi. 7.
134 AXIOMS.
grant that contradictories are true together, it follows that the
contradictory of this very doctrine is true, and that contradic-
tories are not true together.
Against Heraclitus it must be maintained, that all things are
not ever changing, but that in the midst of change there is
something permanent and changeless :' against Anaxagoras,
that, v?hen a subject exchanges any predicate for its contradic-
tory, the latter did not previously exist in it actually, but only
potentially -J^ against Protagoras, that only the perfect sense or
judgment is the criterion of truth, not any sense or judgment
indiscriminately. '
Any doctrine can be verbally denied, but not always mentally
disbelieved ;* and, though some have maintained that contra-
dictories can be true together, yet it may be demonstrated that
they were belied bf their own reason -fi for, if it be objectively
true that the same subject cannot have contradictory predicates,
then, if we take judgment as a subject and belief as a predicate,
it follows, that the same judgment cannot entertain two contra-
dictory beliefs ; and the consciousness of this inability is a re-
cognition of the Axiom. Every understanding, then, recognizes
the Axioms, which thus differ from the Hypotheses,^ and are
the indispensable condition of any opinion or science.'^
' on y«p lariv uKivriToe ne fvmg ° apx4 ""'P' 5" SiaTpevaOijvai ASv-
Seuctbov aiiToie Kai iriiffTsov avTovg. varov . . . ei yap ftrj kvSsxerai H/ia
— Met. iv. 5. virdpxuv Tif aiiTif rd ivavria S
'■' TO AopiaTov BoiKum \kyeiv .... karl do^a SoHy )? t^q A-vn^aatiDQ,
TO yctp Svvafiei ov Kal fi-q kvTEKexeif (pavepbv on aSvvarov &fia vir6\afi-
To dopitTTov ioTU — Met. iv. 4 j also fSdvsiv tov avTbv tlvai Kai firj slvai
Met. i. 7. t6 avTO. — Met. iv. 3.
^ kipQapfikviav Kal \iKti>firipivii>v ^ <ipxV dwiroBETOQ' ^v ydp dvay-
tS>v eTepiDv rd aia9tjT'!]piov Kal Kpirjj- Koiov ix^iv Thv otiovv avvikvTa tSiv
pioj/j Toi)q eTEpovg fiiv vTroXrjTrTeov bvriov, tovto oitK VTToQttriQ, — Ibid.
fiETpov elvaij Toig d* Irkpovg oiix ovk egti d' vjroOeffig o dvdyKrj
v7ro\ji-jrT£ov. oftoitog Ss tovto Xsyoi tlvai St avTb Kal Soxetv dvdyKrj, —
Kal «7rt dya^ou Kal KaKov Kal koXov Post. Anal. i. 10.
Koi alffxpov Kal Tutv aXKwv twv toL' ^ iijv dvdyKrj exEiV Tbv otiovv fia~
ovTiav. — Met. xi. 6. Btjaoiievov, d^iD/jui. — Post. Anal. i.
* dii effTLV hvUTijvai rrpbg t6v e^oj 2. S dk yviopiZsiv dvayKoiov Tip OTt-
\6yoVf dWd TTpbg rbv eVw \6yov ovv yvinpit^ovTif Kal ijKELv fi^oj/ra
OVK dtl. — Anal. Post. i. 10, dvayKoiov. — Met. iv, 3.
AXIOMS. 135
§ 5. How do the Axioms enter science, of which they are
said to be the common principles ? Not as' propositions or pre-
misses, but as the principle of syllogism by which we pass from
premisses to a conclusion.
We may show that the Axiom : The same thing cannot have
contradictory predicates, is equivalent to the dictum, de omni
et nulla, by applying it to the two first moods of the first figure.
For in the afiirmative syllogism,
all B is A
aU C is B
.-. all C is A,
the major premiss may be considered as assigning A, one of two
contradictory predicates, to B ; the minor as recognizing the
identity of B and C ; and the conclusion as affirming, in virtue
of the Axiom, that C cannot possess the contradictory of A.
A negative syllogism can be analyzed in the same manner. In
the syllogism,
no B is A
all C is B
.•.no C is A,
the major premiss ascribes not-A, one of two contradictories, to
B ; the minor recognizes the sameness of B and C ; and the
conclusion, by faith in the Axiom, denies the other contradic-
tory of C. The explanation wUl slightly vary according as we
take different forms of the Axiom.
Their equivalence to the dictum de omni et nulla appears to
have been held by Aristotle from his calling them the Syllo-
gistic principles, or the Demonstrative principles -A and he
seems to mean that they are not employed as premisses, when
he says that they are not expressed but only implied, unless the
conclusiveness of an argument is called in question.^
" irepi tSv diroSeiKTiicwv dpx?>v ° oiSefiia Xafi^avH diroSuKig dW
Xeyiit S' d'TroSuKTiKd.Q, Koi rag Roi.vd.q ri lav Sky Seiiai icai rh av/jfTrBpaa/ia
So^ag £? (5v HiravTcg Sumivovai. — : ovTiiig. — Post. Anal, i. 11. Coin-
Met, lii. 2. Trept tSv ovXKoyianKSiv pare oiS' iv avWoyur/iif Xa/ilSdverat
dpxoiv Tov fi\oiT6<l)ov kariv ItthtkI- rt iari t6 avWeXoyiaBaf del yap
jj/aaBai. — Met. iv. 3. iiXij ^ liepog ij Trporaaig i% &v b avK-
136 AXIOMS.
To make the Axioms major premisses would be to give some
colour to the imputation sometimes cast upon Logic, that she
teaches a cumbrous mode of reasoning of her own, not that
which is taught by nature and practised by the unsophisticated
understanding.
Though barren of consequences themselves, the Axioms
enable us to educe the consequences of other truths ; and
though alone they are insufficient, it would be a mistake to
suppose that we could dispense with their assistance : hence
there is an inaccuracy in the following passage of Locke, which
is otherwise perfectly Aristotelian in its view. " It was not," he
says, "the influence of those maxims which are taken for princi-
ples in Mathematics that hath led the masters of that science
into those wonderful discoveries they have made. Let a man
of good parts know all the maxims generally made use of in
Mathematics never so perfectly, and contemplate their extent
and consequences as much as he pleases, he will by their assist-
ance, I suppose, scarce ever come to know that the square of
the hypothenuse in a right angled triangle is equal to the
squares of the two other sides. The knowledge that the whole
is equal to all its parts, and, if you take equals from equals the
remainders will be equal, helped Mm not, I presume, to this de-
monstration : and a man may, I think, pore long enough on
those axioms, without ever seeing one jot the more of mathe-
matical truths." Essay on Human Understanding, Book iv.
chap. 12, § 15. Again, " The axioms are not the foundations
on which any of the sciences is built ; nor at all useful in helping
men forward to the discovery of unknown truths." — Book iv.
chap. 7, § 11. It is true that poring on the Axioms alone would
not enable us to discover mathematical truths, but it does not
for all that follow that they are utterly useless.* Though un-
productive themselves, they help us to unfold the results of
more prolific data: and without them we could not make a
XoyitTiiog' SeX Se TTjOof rbv a^0Mr/3)j- ^etx^ijffETat' ra yap yevrj rutv ovtiov
Tovvra ft (TvWeXSyitTrat ij ftij rovro, erepa' Kal ra fikv Toig irotroTg rd Si '
diTavraVj 'on' tovto ydp riv ffuXXo- rotf ttoioIq itirapx^L fiovoiQf fitff &v
yuT/jLog. — Post. Anal. ii. 6. SeiKwrai Sid rdv koivUv. — Post.
* dW ovSe Tutv Koiv&v dpxS>v Anal. i. 32.
oiov T ilvai Tivaq l^ 5iv diravra
AXIOMS. 137
single step in deduction, as they constitute in fact the deductive
faculty. Dugald Stewart recognized the distinction between
Axioms and Theses, the latter of which he calls First Princi-
ples, the former Laws of Belief. — (Philosophy of the Human
Mind, part 2, chapters 1, 2.)
Mr. Whewell's Axioms are very different from those of Ari-
stotle. Sometimes they are equivalent to Hypotheses (book x.
5) : sometimes they contain more than the Hypothesis, being
supplementary to the Definitions where these are inadequate j
sometimes the word is used in the stricter sense. Yet, though
thus peculiar in his use of the term, he censures Locke and
Stewart, who affixed a very different meaning to it, for calling
the Axioms barren truisms. This is true in the sense in which
they employed the term. The Axioms are themselves barren
and fruitless, their office being to cause the Theses to fructify.
In Dialectics and Rhetoric a similar relation obtains between
the Topics and the Organa, or specific premisses.
§ 6. The Axiom is not used in all its generality whenever
employed, but only so far as it regards the subject-matter under
discussion :i in Mathematics, for instance, it does not contain
the notion of Identity, but only the Mathematical form of this.
Equality.
The existence and character of the Axioms is indicated by
Logic ; and the laws of reasoning, as traced by General Logic,
may be considered as the development of their simplest form :
they are used by all the sciences -.^ they are discussed and de-
fended by Metaphysics ; and are characteristic of Dialectics.
The Dialectical Maxims or Topics are modifications of the
Axioms, and obtainable by deduction •,^ for they appear to be
the derivative Axioms to which Aristotle alludes.
' vpiivTai liiv iravTCQ, eiri roaov- \ov wtipi^ro iuKvvvai t& Koivd. —
Tov di xpiavTai 'tip' 'oaov airolg Ixa- Anal. Post. 1.11.
vov' TOVTO S' iariv '6aov iir'ix^i to ' ifivau yap cipxv t«^ ™»' aWiav
yivoe irtpl ov ^ipovairdeavoSei^tig. dluaiiaTiov avrt) iravTiav. — Met. iv.
..Met. iv. 3; also Anal. Post. i. 10. 3. The same is asserted by Sir Wm.
^ imKoivaivovai SI T^aaai ai km- Hamilton. " For every maxim of
arrjfiai dXKiiXaiE Bards rA Koivd, leah every Dialectical Place is itself cou-
9j StaKcKTiKV irdaaig, (cat ft ng Ka96- tained within the sphere of one or
138 AXIOMS.
It is the Axiom, the principle that one of two contradictories
must apply to every subject, that constitutes the necessity of
Division. 1
§ 7. Some have assigned all primary truths to Metaphysics :
this cannot be, unless it is the sole science ; for all science rests
on a basis of primary laws. But though, in resting on Theses,
Metaphysics only resembles its sister sciences, it stands in a
peculiar relation to the Axioms. The others investigate as well
as use their respective Theses, but employ the Axioms without
submitting them to an investigation ; for as these principles are
laws of all Being, their investigation belongs to the science of
Being, that is, to Metaphysics or Ontology : by Metaphysics,
therefore, they are investigated as well as employed.
Logic will take cognizance of the Axioms, as, to a certain
degree, it takes cognizance of all truths. An Astronomical con-
clusion, so f^r as it is a conclusion, obeys certain Logical
canons ; so far as it regards the heavenly bodies, it belongs to
Astronomy. In the same way Astronomical principles, so far
as they are principles, exhibit certain Logical attributes : so far
as they refer to the Stars, they are Astronomical. And Logic
stands in a similar relation to the conclusions and principles of
all other sciences. Metaphysics included, whether the principles
are Theses or Axioms. Though the latter, then, are peculiarly
the province of Metaphysics, yet to a certain degree, as well as
all other truths, they would fall under the cognizance of Ijogic.
But a much closer relation than this subsists between the
Axioms and Logic. They are the principles involved in all
reasoning, (called, as we have seen, by Aristotle, avWoyia-riKal
apj^ai, and avoSeLKTiKai a.p)(a.i) that is, they are the very princi-
ples whose consequences and limitations are traced by General
Logic. Metaphysics undertakes their justification and defence
against all assailants ; Logic assumes them as self-evident, and
other of the four logical laws, of fesses to elicit a great variety of eon-
Identity, Contradiction, Excluded elusions from the Axiom.
Middle, and Reason and Conse- ' to 5* Unav ifiTciTrTHv eIq ri)v
quent, of which it is only a subordi- Biaiptaiv av y dvrtKdfiiva, oiiK al-
nate modification." — SeeSirW. H.'s rij^a, dvdyKrj yap. — Anal. Post. ii.
edition of Held, p. 767. Fichte pro- 12.
HYPOTHESES. 139
developes them into the forms of argument and the canons of
syllogism. Through the Axioms, then, Logic is more closely
related to Metaphysics than to the other sciences : it criticizes
both it and them : but while independent of the latter, it bor-
rows from the former some of its ultimate principles.
APPENDIX B.
HYPOTHESES.
§ 1. An Hypothesis is a peculiar principle,^ that is, it differs
from an Axiom, in that it varies in different sciences ; and is the I
element that gives a categorical character to the conclusions,/
by afiirming the reality of the first cause whose effects are de-/
duced, or of the substance whose attributes are proved.^ Had
we merely definitions of the cause and the effect, of the sub-
stance and the attribute, we might indeed demonstrate their
respective connection. But such an effect and attribute would
be purely ideal and imaginary : we should not know their
reality or actual existence, a knowledge that is essential to the
completeness of science. If, however, we know the actual ex-
istence of the first cause or the substance, then by the aid of
definitions we can not only evince the indissoluble connection
of the effect and attribute with such cause and substance, but
also their actual and real existence. The existence of the effect I
and attribute is not assumed in the Hypothesis :' to prove it is 1
the work, and the sole work of Demonstration, for their nature,
or essential character, is assumed in the Definitions. ^
§ 2. It must be observed, that Hypothesis sometimes appears
to signify the contrary of what has been stated ; for a conclu-
' iSia or oUeia dpxri- t^Ti S' ISia inaccurate to use Hypothesis for de-
Kal a. XafijiavcToi ilvai. — Post.Anal. finition, as appears from Post. Anal.
i. 10. i. 2. OTi S" tffri rag jiiv dpxdg dvdy-
' 0e(7ie ^ TO ilvai n fi firi iivai ti kt] XafiPdvuv. — Post. Anal. i. 10.
Xafipdvovaa, vjroBeaig. — Post. Anal. ^ rd St rovriav irdQi] xaff avrd H
i. 2. litv ar)jiaivu FxaaTov Xajifidvovaiv
(Ivai rd &iif(ra koi rde dpxag viro- on 5* tan Sukvvovui. — Poet. Anal,
eiffflat M. — Post. Anal. ii. 8. It is 1. 10.
140 HYPOTHESES.
sion is said to be hypothetical in the absence rather than in the
presence of the Aristotelian Hypothesis : in modern times a
theory is called an Hypothesis before it is established as a
Law — that is, while it consists of Definitions without Hypothe-
ses ; and Aristotle himself calls conditional conclusions hypo-
thetical.' This perhaps may be accounted for from acharacter-
(istic of the Hypothesis that distinguishes it from the Axiom,
its want of recognizable necessity.* Hence it seems to have
been applied to propositions that have scarcely any evidence ;
and a conclusion that rested on such a premiss would be so far
conditional, and, in reference to this premiss, hypothetical.
J There will be no confusion if we remember that when an Hypo-
' thesis is spoken of as a scientific principle, it means that ele-
ment that renders conclusions unconditional and un-hypothe-
tical.
§ 3. Three characteristics, then, are united in the conception
f of the Hypothesis : it is an appropriate principle ; it asserts
; existence or reality ; and its necessity is deficient in evidence.
From this last peculiarity of existential propositions, some mo-
dern writers have maintained that the demonstrative sciences
are hypothetical, not categorical.' Kant maintains that the ex-
istence of Space and Time are inevitably believed, and hence
gives the mathematical sciences a categorical character. He
considers that the want of evidence or subjective necessity in
the Hypothesis of Natural Theology is an important objection
against that science. But there is no apparent reason why a
Being should not be possessed of necessary existence, though
the necessity of its existence be not discoverable to the human
mind. Aristotle merely observes that existential propositions
vary in degrees of evidence.*
§ 4. Arts will be founded on Definitions alone, not on Hypo-
' Categorical and conditional are tlvai Si aurh ical SokeXv dvayKt]. —
opposed as airXiog and el viroBiaeiag. Post. Anal. i. 10.
Post. Anal. i. 22. ' Dugald Stewart.
See the distinction of categorical ' rb yivog pt-fi vtroTiOiaQai tlvai
or absolute and hypothetical neces- hv y favtpbv on iarlv ov yip o/ioi-
sity. De Part. Anim. i. 1 ; also lag SrjXov on o dpiBnog ean Kal 8n
Physic. Ausc. ii. 9. Bcp/ibv Kal \l/vxpov. — Post. Anal.
'' ovK etrn 5' vwoBiaig o dvayKri i. 10.
HYPOTHESES. 141
theses : for the foundation of Productive reasoning is the con-
ception of an end, which does not yet exist, but may exist if
certain means are put into execution, i So the result of Moral
deliberation is a conditional conclusion ; it only asserts that a
certain measure must be adopted^ if we wish to realize a certain
end. It is the duty, however, of Moral Philosophy to show
the possibility of this end, that is, not its actual, but its poten-
tial existence ; which duty is performed when she establishes
the freedom of the will. The will is the efficient cause by
which the end may be realized ; and the propositions which
state its freedom may be regarded as the Ethical Hypothesis,
asserting the potential existence of the Moral Good.
§ 5. Besides the Absolute Hypothesis, there is a Kelative*
Hypothesis which is susceptible of proof, and therefore is not a |
genuine first principle f it is assumed, however, as a principle, '
because the person to whom it is addressed is willing to accept
it without proof. This appears to be the sense in which Plato
uses the word, when he calls the principles of all but the pri-
mary science Hypotheses, meaning merely arbitrary points of
departure, capable of deduction from higher principles.' Under
this head would come what Bacon has called the Axiomata
Media.
A primary law of -any science can be analyzed into two ele-
ments ; one of which defines the character of an original power,
and the other affirms its existence. Though the latter of these
is, properly speaking, the Hypothesis, yet it is sometimes used
to denote the whole truth ;* in which case, perhaps, greater
prominence is given to the existence of the subject-matter than
to its essence.
§ 6. The Aristotelian Hypothesis corresponds to what Mr.
' i} yelp apx4 Toie l>^v rb ov ToXg iiriPaaeiQ re Kai opfiag. — Ibid. 20.
Sk Tb Iffd/tEvojA— De Part. Anim. i. 1. SiA. rb jxv iw' dpxw avcXedvTas
» Post. Anal. i. 10. o-KOTreTv ctXK.' tS viroBktrvav, vovv
^ rb fiiv ^vxh ZwrtXr dvayKoZtrai ovk laxuv. — Ibid.
i^ vvoBkaiiov, rb d" av 'drepov i-ir v SiaXiKTuefi rde v-iroOkait^ avai-
apxvv dwiroGiTov t'oSffa.— Hep. vi. povaa kir' avrrtv rfivdpxhv vopcvi-
19.
rat. — Ibid. vii. 13.
rdc iiiroBkauc Trmovfievog oiiK dp- * Himip kv role p.a6iiimTiKoXi; ai
X&g, dWA. Tif bvn iinoOkauQ, olov ivoOkaug.—mh. Nic. vii. 8.
142 HYPOTHESES.
Mill has called the Collocation of Causes, which is explained in
the following passages : —
" This leads us to a conception which we shall find of great
importance in the interpretation of nature ; that of a Perma-
nent Cause, or original natural agent. There exist in nature a
number of permanent causes, which have subsisted ever since
the human race has been in existence, and for an indefinite and
probably enormous length of time previous. The sun, the earth
and planets, with their various constituents, air, water, and the
other distinguishable substances, whether simple or compound,
of which nature is made up, are such permanent causes . . . We
can give, scientifically speaking, no account of the origin of the
permanent causes themselves. Why these particular natural
agents existed originally and no others, or why they are com-
mingled in such and such proportions, and distributed in such
and such a manner throughout space, is a question we cannot
answer . . . All phaenomena, without exception, which begin to
exist, that is, all except the primeval causes, are effects either
immediate or remote of those primitive facts, or of some combi-
nation of them . . . The whole of the phaenomena of nature
were therefore the necessary, or in other words, the uncondi-
tional, consequences of the original collocation of the Perma-
nent Causes." — System of Logic, book iii. 5.
" It is necessary here to remark, that in this resolution of the
law of a complex effect, the laws of which it is compounded are
not the only elements. It is resolved into the laws of the sepa-
rate causes, together with the fact of their co-existence. The
one is as essential an ingredient as the other ; whether the ob-
ject be to discover the law of the effect, or only to explain it.
To deduce the laws of the heavenly motions, we require not
only to know the law of a rectilineal and that of a gravitative
force, but the existence of both these forces in the celestial
regions, and even their relative amount. The complex laws of
causation are thus resolved into two distinct kinds of elements :
the one simpler laws of causation, the other (in the aptly se-
lected language of Dr. Chalmers) collocations ; the collocations
consisting in the existence of certain agents or powers, in cer-
tain circumstances of place and time." — Book iii. 12.
" Derivative laws, therefore, do not depend solely upon the
HYPOTHESES. 143
ultimate laws into which they are resolvable : they mostly de-
pend upon those ultimate laws and an ultimate fact ; namely,
the mode of co-existence of some of the original elements of
the universe. The ultimate laws of causation might be the
same as at present, and yet the derivative laws completely dif-
ferent, if the causes co-existed in different proportions, or with
any difference in those of their relations by which the effects
are influenced." — Book iii. 16.
The ultimate laws of the Permanent causes assume, in the
Aristotelian Logic, the form of Definitions : the ultimate fact of
the existence of these causes, that gives an unconditional con-
clusion, is expressed in the Hypothesis ; both are called The-
ses ; and, combined with the developing Axioms, tliey are a
sufficient basis of categorical science.
What Mr. Mill has called a Postulate is the Hypothesis.
See note to Post. Anal. ii. 7.
OXFORD :
PRINTED BY E, W. MORRIS.
Cornell University Library
B441.A5 P85
Logic of science : a translation of the
olin
3 1924 028 996 572
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